Hjem
Irina Markinas bilde

Irina Markina

Professor
  • E-postIrina.Markina@uib.no
  • Telefon+47 55 58 28 53
  • Besøksadresse
    Realfagbygget, Allégt. 41
  • Postadresse
    Postboks 7803
    5020 Bergen
  • Real Analysis and Potential Theory
  • PDE
  • Fluid Mechanics and Mathematical Physics
  • Sub-Riemannian and Sub-Lorentzian geometry

 

 

Tidsskriftartikler
  • Furutani, Kenro; Markina, Irina. 2017. Complete classification of pseudo H-type Lie algebras: I. Geometriae Dedicata. Published ahead of print: 1-29. doi: 10.1007/s10711-017-0225-1
  • Godoy Molina, Mauricio; Kruglikov, Boris; Markina, Irina; Vasiliev, Alexander. 2017. Rigidity of 2-step carnot groups. Journal of Geometric Analysis. Published ahead of print: 1-25. Publisert 2017-06-19. doi: 10.1007/s12220-017-9875-3
  • Brakalova, Melkana A.; Markina, Irina; Vasiliev, Alexander. 2016. Modules of systems of measures on polarizable Carnot groups. Arkiv för matematik. 54: 371-401. doi: 10.1007/s11512-016-0242-6
  • Chang, Der-Chen; Markina, Irina; Wang, Wei. 2016. On the Hodge-type decomposition and cohomology groups of k-Cauchy-Fueter complexes over domains in the quaternionic space. Journal of Geometry and Physics. 107: 15-34. doi: 10.1016/j.geomphys.2016.04.016
  • Markina, Irina; Vasiliev, Alexander. 2016. Evolution of smooth shapes and integrable systems. Computational methods in Function Theory. 16: 203-229. doi: 10.1007/s40315-015-0133-z
  • Chitour, Yacine; Godoy Molina, Mauricio; Kokkonen, Petri; Markina, Irina. 2015. Rolling against a sphere: the non-transitive case. Journal of Geometric Analysis. Published ahead of print. 21 sider. doi: 10.1007/s12220-015-9638-y
  • Furutani, Kenro; Markina, Irina; Vasiliev, Alexander. 2015. Free nilpotent and H-type Lie algebras. Combinatorial and orthogonal designs. Journal of Pure and Applied Algebra. 219: 5467-5492. doi: 10.1016/j.jpaa.2015.05.027
  • Grong, Erlend; Markina, Irina; Vasiliev, Alexander. 2015. Sub-Riemannian Geometry on Infinite-Dimensional Manifolds. Journal of Geometric Analysis. 25: 2474-2515. doi: 10.1007/s12220-014-9523-0
  • Autenried, Christian; Markina, Irina. 2014. Sub-Riemannian geometry of Stiefel manifolds. SIAM Journal of Control and Optimization. 52: 939-959. doi: 10.1137/130922537
  • Furutani, Kenro; Markina, Irina. 2014. Existence of lattices on general H-type groups. Journal of Lie theory. 24: 979-1011.
  • Khajeh Salehani, Mahdi; Markina, Irina. 2014. Controllability on Infinite-Dimensional Manifolds: A Chow-Rashevsky Theorem. Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. 134: 229-246. Publisert 2014-04-29. doi: 10.1007/s10440-014-9880-5
  • Chang, Der-Chen; Markina, Irina; Wang, Wei. 2013. On the Cauchy-Szegö kernel for quaternion siegel upper half-space. Complex Analysis and Operator Theory. 7: 1623-1654. doi: 10.1007/s11785-012-0282-2
  • Godoy Molina, Mauricio; Korolko, Anna; Markina, Irina. 2013. Sub-semi-Riemannian geometry of general H-type groups. Bulletin des Sciences Mathématiques. 137: 805-833. doi: 10.1016/j.bulsci.2013.05.005
  • Godoy Molina, Mauricio; Grong, Erlend; Markina, Irina; Leite, Fátima Silva. 2012. An intrinsic formulation of the problem on rolling manifolds. Journal of dynamical and control systems. 18: 181-214. doi: 10.1007/s10883-012-9139-2
  • Markina, Irina; Godoy Molina, Mauricio. 2012. Sub-Riemannian geodesics and heat operator on odd dimensional spheres. Analysis and Mathematical Physics. 2: 123-147. doi: 10.1007/s13324-012-0028-3
  • Chang, Der-chen; Markina, Irina; Vasiliev, Alexander. 2011. Hopf fibration: Geodesics and distances. Journal of Geometry and Physics. 61: 986-1000. doi: 10.1016/j.geomphys.2011.01.011
  • Korolko, Anna; Markina, Irina. 2011. SEMI-RIEMANNIAN GEOMETRY WITH NONHOLONOMIC CONSTRAINTS. Taiwanese journal of mathematics. 15: 1581-1616.
  • Markina, Irina; Godoy Molina, Mauricio. 2011. Sub-Riemannian geometry of parallelizable spheres. Revista matemática iberoamericana. 27: 997-1022.
  • Chang, Der-chen; Markina, Irina; Vasiliev, Alexander. 2010. Modified action and differential operators on the 3-D sub-Riemannian sphere. Asian Journal of Mathematics. 14: 439-473.
  • Korolko, Anna; Markina, Irina. 2010. Geodesics on H-type Quaternion Groups with Sub-Lorentzian Metric and Their Physical Interpretation. Complex Analysis and Operator Theory. 4: 589-618. doi: 10.1007/s11785-010-0079-0
  • Markina, Irina; Vasiliev, Alexander. 2010. Virasoro algebra and dynamics in the space of univalent functions. Contemporary Mathematics. 525: 85-116.
  • Calin, Ovidiu; Chang, Der-chen; Markina, Irina. 2009. SubRiemannian Geometry on the Sphere S-3. Canadian Journal of Mathematics - Journal Canadien de Mathematiques. 61: 721-739.
  • Calin, Ovidiu; Chang, Der-chen; Markina, Irina. 2009. Geometric analysis on H-type groups related to division algebras. Mathematische Nachrichten. 282: 44-68. doi: 10.1002/mana.200710721
  • Chang, Der-Chen; Markina, Irina; Vasiliev, Alexander. 2009. Sub-Riemannian geodesics on the 3-D sphere. Complex Analysis and Operator Theory. 3: 361-377. doi: 10.1007/s11785-008-0089-3
  • Korolko, Anna; Markina, Irina. 2009. Nonholonomic lorentzian geometry on some H-type groups. Journal of Geometric Analysis. 19: 864-889. doi: 10.1007/s12220-009-9088-5
  • Chang, Der-Chen; Markina, Irina. 2008. Geometric analysis on quaternion anisotropic Carnot groups. Doklady. Mathematics. 77: 124-129. doi: 10.1007/s11472-008-1031-2
  • Chang, Der-chen; Markina, Irina. 2008. Quaternion H-type group and differential operator Delta(lambda). Science in China Series A: Mathematics. 51: 523-540. doi: 10.1007/s11425-007-0133-1
  • Chang, Der-chen; Markina, Irina; Vasiliev, Alexander. 2008. Sub-Lorentzian geometry on anti-de Sitter space. Journal des Mathématiques Pures et Appliquées. 90: 82-110. doi: 10.1016/j.matpur.2008.02.012
  • Chang, Der-chen; Markina, Irina. 2007. Anisotropic quaternion carnot groups: Geometric analysis and green function. Advances in Applied Mathematics. 39: 345-394. doi: 10.1016/j.aam.2007.02.002
  • Hidalgo, Ruben; Markina, Irina; Vasiliev, Alexander. 2007. Finite dimensional grading of the Virasoro algebra. Georgian Mathematical Journal. 14: 419-434.
  • Markina, Irina; Meneses, Rodrigo; Vasiliev, Alexander. 2007. On a Saffman-Taylor problem in an infinite wedge. Applicable Analysis. 86: 239-250. doi: 10.1080/00036810601148224
  • Markina, Irina; Prokhorov, Dmitri; Vasiliev, Alexander. 2007. Sub-Riemannian geometry of the coefficients of univalent functions. Journal of Functional Analysis. 245: 475-492. doi: 10.1016/j.jfa.2006.09.013
  • Chang, Der-Chen; Markina, Irina. 2006. Geometric analysis on quaternion H-type groups. Journal of Geometric Analysis. 16: 265-294.
  • Markina, Irina; Vodopyanov, Sergey. 2006. On value distribution for quasimeromorphic mappings on H-type Carnot groups. Bulletin des Sciences Mathématiques. 130: 467-523.
Bokkapitler
  • Markina, Irina. 2016. Geodesics in Geometry With Constraints and Applications. pp 153-314, sider 153-314. I:
    • Bahns, Dorothea; Bauer, Wolfram; Witt, Ingo. 2016. Quantization, PDEs, and Geometry. The interplay of Analysis and Mathematical Physics. Birkhäuser Verlag. 314 sider. ISBN: 978-3-319-22407-7.
  • Markina, Irina; Vasiliev, Alexander. 2013. Löwner-Kufarev Evolution in the Segal-Wilson Grassmannian. -, sider 367-377. I:
    • Kielanowski, Piotr; Ali, S. Twareque; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore. 2013. Geometric Methods in Physics. Springer Science+Business Media B.V.. ISBN: 978-3-0348-0447-9.
  • Grong, Erlend; Markina, Irina; Vasiliev, Alexander. 2012. Sub-Riermannian structures corresponding to Kählerian metrics on the universal Teichmüller space and curve. -, sider 97-116. I:
    • Szynal, Jan. 2012. 60 years of Analytic Functions in Lublin. In memory of our professors and friends Jan G. Krzyz, Zdzislaw Lewandowski and Wojciech Szapiel. ISBN: 978-83-62074-62-4.
  • Korolko, Anna; Markina, Irina. 2011. Nonholonomic semi-Riemannian geometry with examples on H-type groups. article, sider 43-56. I:
    • Santana, Ana Paula. 2011. Textos de matemática : mathematical papers in honour of Fátima Silva Leite. ISBN: 978-972-8564-47-6.
  • Molina, Mauricio Godoy; Grong, Erlend; Leite, Fátima Silva; Markina, Irina. 2011. Rolling manifolds : an intrinsic perspective. article, sider 71-84. I:
    • Santana, Ana Paula. 2011. Textos de matemática : mathematical papers in honour of Fátima Silva Leite. ISBN: 978-972-8564-47-6.
  • Calin, Ovidiu; Chang, Der-chen; Markina, Irina. 2009. Generalized Hamilton-jacobi Equation and Heat kernel. chapter 3, sider 49-76. I:
    • Vasiliev, Alexander; Gustafsson, Björn. 2009. Analysis and Mathematical Physics. Birkhäuser Verlag. 514 sider. ISBN: 978-3-7643-9905-4.

Se fullstendig oversikt over publikasjoner i CRIStin.

  1. I.Markina: The change of variable that preserves the differential properties of Functions. Sibirsk. Mat. Zh. 31 (1990), no. 3, 73-84; translation in Siberian Math. J. 31 (1990), no. 3, 422-432.
  2. I.Markina: The multiplier space M(Hpm->Hq1). Applications of functional analysis to problems of mathematical physics, 106-120; Akad Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1990.
  3. I.Markina, S.K.Vodop'yanov: Exceptional sets for solutions of subelliptic equations. Sibirsk. Mat. Zh. 36 (1995), no. 4, 805-818; translation in Siberian Math. J. 36 (1995), no. 4, 694-706.
  4. I.Markina, S.K.Vodop'yanov: Fundamentals of the nonlinear potential theory for subelliptic equations. Sobolev spaces and related problems of analysis, 100-160; Trudy Inst. Mat., 31, Izdat. Ross. Akad. Nauk Sib. Otd.Inst. Mat., Novosibirsk, 1996.
  5. I.Markina: Classification of sub-Riemannian manifolds.- Algebra,geometry, analysis and mathematical physics (Novosibirsk, 1996), 176-178; Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 1997.
  6. I.Markina, S.K.Vodop'yanov: Fundamentals of the nonlinear potential theory for subelliptic equations. I. Siberian Adv. Math. 7 (1997), no. 1, 32-62.
  7. I.Markina, S.K.Vodop'yanov: Fundamentals of the nonlinear potential theory for subelliptic equations. II.- Siberian Adv. Math. 7 (1997), no. 2, 18-63.
  8. I.Markina, S.K.Vodop'yanov: Foundations of the nonlinear potential theory of subelliptic equations. Dokl. Acad. Sci. Rus. 359 (1998), no. 2, 155-158.
  9. I.Markina, S.K.Vodop'yanov: Classification of sub-Riemannian manifolds. Sibirsk. Mat. Zh. 39 (1998), no. 6, 1271-1289; translation in Siberian Math. J. 39 (1998), no. 6, 1096-1111.
  10. I.Markina, S.K.Vodop'yanov: Local estimates of change of mappings with bounded s-distortion on the Carnot groups.- Proceedings of the 11-th Siberian school: Algebra, geometry, analysis and mathematical physics. (Novosibirsk, August 1-9, 1998) Novosibirsk. 1999, 28-53.
  11. I.Markina: On the coincidence p-module of a family of curves and p-capacity of a condenser in the metric space with controlled geometry. Proceedings of the 11-th Siberian school: Algebra, geometry, analysis and mathematical physics. (Novosibirsk, August 1-9, 1998) Novosibirsk, 1999, 83 - 92.
  12. I.Markina: On local homeomorphism of mappings with bounded distortion with the coefficient of distortion close to identity. Sci. Ser. A Math. Sci. (N.S.) 8 (2002), 21-42.
  13. I.Markina: On coincidence of p-module of a family of curves and p-capacity on the Carnot group.- Rev. Mat. Iberoamericana 19 (2003), no. 1, 143-160.
  14. I.Markina, A.Vasil'ev: On the geometry of Hele-Shaw flows with small surface tension. Interfaces Free Boundaries 5 (2003), no. 2, 183-192.
  15. I.Markina: Extremal lengths for mappings with bounded s-distortion on Carnot groups. Bol. Soc. Mat. Mexicana (3) 9 (2003), no. 1, 89-108.
  16. I.Markina: Hausdorff measure of the singular set of quasiregular maps on Carnot groups.  Int. J. Math. Math. Sci. 35 (2003), 2203-2220.
  17. I.Markina: Extremal length for quasiregular mappings on Heisenberg groups. J.Math. Anal. Appl. 284 (2003), no. 2, 532-547.
  18. I.Markina, A.Vasil'ev: Long-pin perturbations of the trivial solution for Hele-Shaw corner flows. Sci. Ser. A Math.  Sci. (N.S.) 9 (2003), 33-43.
  19. I.Markina: Extremal widths on homogeneous groups. Complex Variables 48 (2003), no. 11, 947 - 960.
  20. I.Markina: P-module of vector measures in domains with intrinsic metric on Carnot groups. Tohoku Math.  J. 54 (2004), no. 4, 553-569.
  21. I.Markina, A.Vasil’ev: Explicit solutions for the Hele-Shaw corner flows. Euro. J. Appl. Math. 15, (2004), no. 6, 781-789.
  22. I.Markina, S.Vodop´yanov: On value distribution for quasimeromorphic mappings on polarizable Carnot groups. Dokl. Acad. Sci. Rus.  403 (2005), no. 3, 300-304.
  23. I.Markina: Module of vector measures on the Heisenberg group. Contemp. Math., 382 (2005), 291-304.
  24. I.Markina: Singularities of quasiregular mappings on Carnot groups. Sc. Ser. A Math.  Sci. (N.S.) 11, (2005), 69-81.
  25. I.Markina, D.Ch.Chang: Geometric analysis on quaternion $H$-type groups. J. Geom. Anal. 16, (2006), no. 2, 265-294.
  26. I.Markina, S.Vodop´yanov: On value distribution for quasimeromorphic mappings on H-type Carnot groups. Bull. Sci. math. 130 (2006), 467-523.
  27. I.Markina, R.Meneses, A.Vasil’ev: Generalizations of Kadanoff's solution of the Saffman-Taylor problem in a wedge. Appl. Anal. 86 (2007), no 2, 239-250.
  28. I.Markina, V.D.Prokhorov, A.Vasil’ev: Sub-Riemannian geometry of the coefficients of univalent functions. J. Func. Anal. 245 (2007), 475-492.
  29. I.Markina, R.Hidalgo, A.Vasil’ev: Finite dimensional grading on the Virasoro algebra. Georgian Mathematical Journal 14 (2007), no. 3, 419-434.
  30. I.Markina, D.Ch.Chang: Anisotropic quaternion Carnot groups: geometric analysis and Green’s function. Adv. Appl. Math. 39 (2007), 345-394.
  31. I.Markina, D.Ch.Chang: Geometric analysis on anisotropic quaternion Carnot groups. Dokl. Acad. Sci. Rus. 77 (2008), no. 1, 124-129.
  32. I.Markina, D.Ch.Chang: Quaternion H-type group and differential operator ∆_l. Science in China Ser. A. Mathematics. 51 (2008), no. 4,  523-540.
  33. I.Markina, D.Ch.Chang, A. Vasiliev. Sub-Lorentzian geometry on anti-de Sitter space.  J. Math. Pures Appl. (9) 90 (2008), no. 1,  82-110.
  34. I.Markina, D.Ch.Chang, A.Vasiliev: Sub-Riemannian geodesics on 3-D sphere. Complex Anal. Oper. Theory. 3 (2) (2008), 361-377
  35. I.Markina, D.Ch.Chang, O. Calin: Geometric analysis on H-type groups related to division algebras. Math. Nach.  282 (2009), no. 1, 44-68
  36. I.Markina, D.Ch.Chang, O. Calin: Generalized Hamilton - Jacobi equation and heat kernel on  step two nilpotent Lie groups. Proceedings of the conference”Harmonic and complex analysis and its applications” Anal. Math. Phys. Trends in Math. (2009), 49-76
  37. I.Markina, D.Ch.Chang, O. Calin: Sub-Riemannian geometry on the sphere S^3. Can. J. Math. 61 (4) 2009, 721-739

 

Education:

Graduated from Novosibirsk State University in 1986

Degrees:

  • M.Sci., June 3, 1986, in the Novosibirsk State University, Special studies in Advanced Mathematics. Thesis title: "Change-variable formula for functional spaces with fractional derivatives", 45 pp., supervisor Prof. S.K. Vodopyanov.
  • Ph.D., November 15, 1995, in the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University (Candidate in Physics and Mathematics) Thesis title: "Nonlinear potential theory of subelliptic equations", 180 pp. supervisor Prof. S.K. Vodopyanov

 

Employment:

  • 2008-present: Professor, University of Bergen, Norway.
  • 2008: Associate Professor, University of Bergen, Norway.
  • 2007-2008: Researcher, UNIFOB AS v/ Unifob petroleum (temporary position), University of Bergen, Bergen, Norway.
  • 2006: Associate Professor (temporary position), University of Bergen, Bergen, Norway.
  • 2005: Full Professor, University of Valparaiso, Valparaiso, Chile.
  • 2001-2005: Visiting Professor, Department of Mathematics of Technical University Federico Santa Maria, Valparaiso, Chile.
  • 2000: Research Fellow, The Mittag-Leffler Institute, Stockholm, Sweden.
  • 1999-2000: Associate Professor, Department of Mathematics, Siberian State University of Telecommunication and Information, Novosibirsk, Russia.
  • 1996-1999: Assistant Professor, Department of Mathematics, Novosibirsk State University, Russia.
  • 1991-1996: Assistant Professor, College of Informatics, Novosibirsk State University, Russia.
  • 1986-1991: Post-graduate course, Sobolev Institute of Mathematics, of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia.

 

Languages:

Russian, English, Spanish, Norwegian

 

Professional Membership:

  • American Mathematical Society, since 2001
  • Mathematical Society of Chile, 2001-2006

 

Other Professional Activities:

  • 2009: Main organizer of the "Norwegian Fall School in Analysis for PhD Students and Young Researchers" Trondheim, September 10-13.
  • 2008-2011: Principal coordinator of the NordForsk Research Network “Analysis and Application”
  • 2003-2005: Responsible for the Department’s Mathematical Colloquium, Technical University Federico Santa Maria, Valparaiso, Chile.
  • 1996-2000: Administrative assistant, Division of Mathematical Analysis, Department of Mathematics, Novosibirsk State University, Russia.
  • 1992-1995: Administrative assistant at the College of Informatics, Novosibirsk State University, Russia.

 

 

 

RESEARCH NETWORK “ANALYSIS and APPLICATIONS”

Irina Markina is the Principal coordinator of the NordForsk Research Network “Analysis and Applications”. The purpose of the network is to promote mobility and cooperation between analysts in the Nordic countries. About 2/3 of the funding is for workshops, seminars and similar events, the rest is for mobility scholarships. The network “Analysis and Applications” is open for researchers and students in analysis in the Nordic countries, Estonia and Northern-West Russia (St. Petersburg). Read more on the research network web-site.

 

GRANTS:

 

  • 2008: Grant of NordForsk for Research Groups Network “Analysis and Applications”, Norway.
  • 2007: Grant NFR – Bilat USA-Norway. (Norwegian Research Council) #180275/D15, Norway.
  • 2005:  Grant FONDECYT # 7050181 –International cooperation, Chile.
  • 2004:  Grant FONDECYT # 7040027 –International cooperation, Chile.
  • 2004-2007: Grant FONDECYT # 1040333– Council for the Development of Science and Technology of Chile, Chile.
  • 2003: Grant FONDECYT # 7030010 –International cooperation, Chile.
  • 2002-2003: Grant FONDECYT # 1020067– Council for the Development in Science and Technology of Chile, Chile.
  • 1996-1997: Grant of Russian Ministry of Superior Education for participation of young researchers in International Conferences, Novosibirsk State University, Novosibirsk, Russia.