• Real Analysis and Potential Theory
• PDE
• Fluid Mechanics and Mathematical Physics
• Sub-Riemannian and Sub-Lorentzian geometry

 

 

Vitenskapelig artikkel

• Der-Chen Chang; Irina Markina; Alexander Vasiliev (2009). Sub-Riemannian geodesics on the 3-D sphere. (ekstern lenke)
• Der-Chen Chang; Irina Markina; Wei Wang (2013). On the Cauchy-Szegö kernel for quaternion siegel upper half-space. (ekstern lenke)
• Irina Markina; Mauricio Godoy Molina (2012). Sub-Riemannian geodesics and heat operator on odd dimensional spheres. (ekstern lenke)
• Der-chen Chang; Irina Markina; Alexander Vasiliev (2008). Sub-Lorentzian geometry on anti-de Sitter space. (ekstern lenke)
• Velimir Jurdjevic; Irina Markina; F Silva Leite (2019). Extremal Curves on Stiefel and Grassmann Manifolds. (ekstern lenke)
• Bruno Franchi; Irina Markina (2023). Exceptional families of measures on Carnot groups. (ekstern lenke)
• Knut Hüper; Irina Markina; Fátima Silva Leite (2021). A lagrangian approach to extremal curves on stiefel manifolds. (ekstern lenke)
• Der-Chen Chang; Irina Markina; Wei Wang (2019). The Laguerre calculus on the nilpotent Lie groups of step two. (ekstern lenke)
• Erlend Grong; Irina Markina (2023). Harmonic maps into sub-Riemannian Lie groups. (ekstern lenke)
• Kenro Furutani; Irina Markina (2021). Automorphism groups of pseudo H-type algebras. (ekstern lenke)
• Yacine Chitour; Mauricio Godoy Molina; Petri Kokkonen et al. (2015). Rolling against a sphere: the non-transitive case. (ekstern lenke)
• Der-Chen Chang; Irina Markina (2006). Geometric analysis on quaternion H-type groups. (ekstern lenke)
• Anna Korolko; Irina Markina (2010). Geodesics on H-type Quaternion Groups with Sub-Lorentzian Metric and Their Physical Interpretation. (ekstern lenke)
• Irina Markina; Dmitri Prokhorov; Alexander Vasiliev (2007). Sub-Riemannian geometry of the coefficients of univalent functions. (ekstern lenke)
• Der-Chen Chang; Irina Markina; Wei Wang (2016). On the Hodge-type decomposition and cohomology groups of k-Cauchy-Fueter complexes over domains in the quaternionic space. (ekstern lenke)
• Kenro Furutani; Irina Markina (2017). Complete classification of pseudo H-type Lie algebras: I. (ekstern lenke)
• V. Jurdjevic; Irina Markina; Leite Silva Leite (2023). Symmetric Spaces Rolling on Flat Spaces. (ekstern lenke)
• Mauricio Godoy Molina; Erlend Grong; Irina Markina (2019). Submersions and curves of constant geodesic curvature. (ekstern lenke)
• Irina Markina; Mauricio Godoy Molina; Kenro Furutani et al. (2018). Lie algebras attached to Clifford modules and simple graded Lie algebras. (ekstern lenke)
• Irina Markina; Mauricio Godoy Molina (2011). Sub-Riemannian geometry of parallelizable spheres. (ekstern lenke)
• Mauricio Godoy Molina; Boris Kruglikov; Irina Markina et al. (2017). Rigidity of 2-step carnot groups. (ekstern lenke)
• Irina Markina; Matteo Raffaelli (2019). Flat approximations of hypersurfaces along curves. (ekstern lenke)
• Anna Korolko; Irina Markina (2009). Nonholonomic lorentzian geometry on some H-type groups. (ekstern lenke)
• Ovidiu Calin; Der-chen Chang; Irina Markina (2009). SubRiemannian Geometry on the Sphere S-3. (ekstern lenke)
• Mauricio Godoy Molina; Irina Markina (2021). Sub-riemannian geodesics on nested principal bundles. (ekstern lenke)
• Knut Hüper; Irina Markina; Fátima Silva Leite (2021). An extrinsic approach to sub-riemannian geodesics on the orthogonal group. (ekstern lenke)
• Mauricio Godoy Molina; Erlend Grong; Irina Markina et al. (2012). An intrinsic formulation of the problem on rolling manifolds. (ekstern lenke)
• Irina Markina (2017). Sub-riemannian geometry and hypoelliptic operators. (ekstern lenke)
• Melkana A. Brakalova; Irina Markina; Alexander Vasil'ev (2017). Extremal functions for modules of systems of measures. (ekstern lenke)
• Mauricio Godoy Molina; Anna Korolko; Irina Markina (2013). Sub-semi-Riemannian geometry of general H-type groups. (ekstern lenke)
• Irina Markina; Fátima Silva Leite (2016). Introduction to the intrinsic rolling with indefinite metric. (ekstern lenke)
• Christian Autenried; Kenro Furutani; Irina Markina et al. (2018). Pseudo-metric 2-step nilpotent Lie algebras. (ekstern lenke)
• Boris Khesin; René Langøen; Irina Markina (2025). Curvatures of measure-preserving diffeomorphism groups of non-orientable surfaces. (ekstern lenke)
• Markus Schlarb; Knut Hüper; Irina Markina et al. (2023). Rolling Stiefel Manifolds Equipped with α-Metrics. (ekstern lenke)
• Irina Markina; Alexander Vasiliev (2010). Virasoro algebra and dynamics in the space of univalent functions. (ekstern lenke)
• Irina Markina; Alexander Vasiliev (2016). Evolution of smooth shapes and integrable systems. (ekstern lenke)
• Irina Markina; Rodrigo Meneses; Alexander Vasiliev (2007). On a Saffman-Taylor problem in an infinite wedge. (ekstern lenke)
• Der-chen Chang; Irina Markina (2007). Anisotropic quaternion carnot groups: Geometric analysis and green function. (ekstern lenke)
• Ovidiu Calin; Der-chen Chang; Irina Markina (2009). Geometric analysis on H-type groups related to division algebras. (ekstern lenke)
• Mahdi Khajeh Salehani; Irina Markina (2014). Controllability on Infinite-Dimensional Manifolds: A Chow-Rashevsky Theorem. (ekstern lenke)
• Der-chen Chang; Irina Markina; Alexander Vasiliev (2011). Hopf fibration: Geodesics and distances. (ekstern lenke)
• Kenro Furutani; Irina Markina (2014). Existence of lattices on general H-type groups. (ekstern lenke)
• Kenro Furutani; Irina Markina; Alexander Vasiliev (2015). Free nilpotent and H-type Lie algebras. Combinatorial and orthogonal designs. (ekstern lenke)
• Kenro Furutani; Irina Markina (2019). Complete classification of pseudo H-type algebras: II. (ekstern lenke)
• Der-Chen Chang; Irina Markina (2008). Geometric analysis on quaternion anisotropic Carnot groups. (ekstern lenke)
• Wolfram Bauer; André Froehly; Irina Markina (2020). Fundamental solutions of a class of ultra-hyperbolic operators on pseudo H-type groups. (ekstern lenke)
• Melkana A. Brakalova; Irina Markina; Alexander Vasiliev (2016). Modules of systems of measures on polarizable Carnot groups. (ekstern lenke)
• Der-chen Chang; Irina Markina; Alexander Vasiliev (2010). Modified action and differential operators on the 3-D sub-Riemannian sphere. (ekstern lenke)
• Der-chen Chang; Irina Markina (2008). Quaternion H-type group and differential operator Delta(lambda). (ekstern lenke)
• Anna Korolko; Irina Markina (2011). SEMI-RIEMANNIAN GEOMETRY WITH NONHOLONOMIC CONSTRAINTS. (ekstern lenke)
• Erlend Grong; Irina Markina; Alexander Vasiliev (2015). Sub-Riemannian Geometry on Infinite-Dimensional Manifolds. (ekstern lenke)
• René Langøen; Irina Markina; Alexander Solynin (2024). Stokes Graphs of the Rabi Problem with Real Parameters. (ekstern lenke)
• Irina Markina; Sergey Vodopyanov (2006). On value distribution for quasimeromorphic mappings on H-type Carnot groups. (ekstern lenke)
• Ruben Hidalgo; Irina Markina; Alexander Vasiliev (2007). Finite dimensional grading of the Virasoro algebra. (ekstern lenke)
• Christian Autenried; Irina Markina (2014). Sub-Riemannian geometry of Stiefel manifolds. (ekstern lenke)

Vitenskapelig bokkapittel

• Erlend Grong; Irina Markina; Alexander Vasiliev (2012). Sub-Riermannian structures corresponding to Kählerian metrics on the universal Teichmüller space and curve. (ekstern lenke)
• Irina Markina; Alexander Vasiliev (2013). Löwner-Kufarev Evolution in the Segal-Wilson Grassmannian. (ekstern lenke)
• Mauricio Godoy Molina; Erlend Grong; Fátima Silva Leite et al. (2011). Rolling manifolds : an intrinsic perspective. (ekstern lenke)
• Irina Markina (2016). Geodesics in Geometry With Constraints and Applications. (ekstern lenke)
• Anna Korolko; Irina Markina (2011). Nonholonomic semi-Riemannian geometry with examples on H-type groups. (ekstern lenke)
• Ovidiu Calin; Der-chen Chang; Irina Markina (2009). Generalized Hamilton-jacobi Equation and Heat kernel. (ekstern lenke)

Innledning

• Sigbjørn Hervik; Boris Kruglikov; Irina Markina et al. (2022). Geometry, Lie Theory and Applications: The Abel Symposium 2019. (ekstern lenke)

Konferanseforedrag

• René Langøen; Irina Markina; Alexander Solynin (2023). Stokes graphs of the Rabi problem with real parameters. (ekstern lenke)

Doktorgradsavhandling

• Mauricio Godoy Molina; Irina Markina (2011). Sub-Riemannian geometry of spheres and rolling of manifolds. (ekstern lenke)
• Anastasia Frolova; Irina Markina (2017). Analytical, combinatorial and topological properties of quadratic differentials and their applications. (ekstern lenke)

Antologi

• Sigbjørn Hervik; Boris Kruglikov; Irina Markina et al. (2022). Geometry, Lie Theory and Applications: The Abel Symposium 2019. (ekstern lenke)

Se en full 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

 

 

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.