Areas of expertise
- Real And Complex Functions (Incl. Several Variables) 010111
- Algebraic And Differential Geometry 010102
Publications
- Isaev, A 2018, 'On necessary and sufficient conditions for the Kobayashi hyperbolicity of tube domains in C2', Journal of Mathematical Analysis and Applications, vol. 460, no. 1, pp. 58-62pp.
- Isaev, A & Kruglikov, B 2017, 'On the symmetry algebras of 5-dimensional CR-manifolds', Advances in Mathematics, vol. 322, pp. 530-564pp.
- Isaev, A 2016, 'Effective Transitive Actions of the Unitary Group on Quotients of Hopf Manifolds', Journal of Geometric Analysis, DOI: 10.1007/s12220- 016-9744-5, 6 pages (online publication).
- Isaev, A 2016, 'On homogeneous hypersurfaces in C3', Journal of Geometric Analysis, DOI: 10.1007/s12220-016-9750-7, 11 pages (online publication).
- Isaev, A 2017, 'Homogeneous Kobayashi-hyperbolic manifolds with automorphism group of subcritical dimension [IN PRESS]', Complex Variables and Elliptic Equations, vol. Online, pp. 1-16, DOI: 10.1080/17476933.2017.1403430.
- Isaev, A 2016, 'On the CR-curvature of Levi degenerate tube hypersurfaces', Methods and Applications of Analysis, vol. 23, no. 4, pp. 317-328pp.
- Isaev, A 2016, 'Affine rigidity of Levi degenerate tube hypersurfaces', Journal of Differential Geometry, vol. 104, no. 1, pp. 111-141.
- Isaev, A 2016, 'On the Kobayashi hyperbolicity of tube domains in C-2', Journal of Mathematical Analysis and Applications, vol. 434, no. 1, pp. 1007-1010pp.
- Isaev, A 2016, 'A criterion for isomorphism of Artinian Gorenstein algebras', Journal of Commutative Algebra, vol. 8, no. 1, pp. 89-111.
- Alper, J & Isaev, A 2016, 'Associated forms and hypersurface singularities: The binary case', Journal fur Reine und Angewandte Mathematik, published online, DOI: 10.1515/crelle-2016-0008.
- Alper, J, Isaev, A & Kruzhilin, N 2016, 'ASSOCIATED FORMS OF BINARY QUARTICS AND TERNARY CUBICS', Transformation Groups, vol. 21, no. 3, pp. 593–618.
- Isaev, A & Kruglikov, B 2016, 'A short proof of the Dimension Conjecture for real hypersurfaces in C2', Proceedings of the American Mathematical Society, vol. 144, no. 10, pp. 4395–4399.
- Isaev, A 2016, 'Examples of reconstruction of homogeneous isolated hypersurface singularties from their Milnor algebras', Complex Analysis and Dynamical Systems VI, 2013, ed. Dennis DeTurck, Contemporary Mathematics, vol. 667, American Mathematical Society, United States of America, pp. 125-140.
- Isaev, A 2016, 'On the contravariant of homogeneous forms arising from isolated hypersurface singularities', International Journal of Mathematics, vol. 27, no. 11, 1650097 (14pages, electronic).
- Isaev, A 2015, 'Proper actions of high-dimensional groups on complex manifolds', Bulletin of Mathematical Sciences, vol. 5, no. 2, pp. 251-285.
- Isaev, A 2015, 'A complex-analytic proof of a criterion for isomorphism of Artinian Gorenstein algebras', Complex Analysis and its Synergies, vol. 1, no. 1, pp. 1-10.
- Isaev, A 2015, 'Duality for binary quartics and ternary cubics arising from their Milnor Algebras', REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, vol. 60, no. 4, pp. 471-480.
- Isaev, A 2014, 'On a family of real hypersurfaces in a complex quadric', Differential Geometry and its Applications, vol. 33, pp. 259-266.
- Alper, J & Isaev, A 2014, 'Associated forms in classical invariant theory and their applications to hypersurface singularities', Mathematische Annalen, vol. 360, pp. 799-823.
- Eastwood, M & Isaev, A 2014, 'Invariants of Artinian Gorenstein algebras and isolated hypersurface singularities', in Geoffrey Mason, Ivan Penkov, Joseph A. Wolf (eds.), Developments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics 38, pp. 159-173. Springer Science+Business Media, Switzerland.
- Isaev, A & Kruzhilin, N 2014, 'Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras', Proceedings of the American Mathematical Society, vol. 142, no. 2, pp. 581-590.
- Isaev, A 2014, 'The reconstruction and recognition problems for homogeneous hypersurface singularities', Japanese-Australian Workshop on Real and Complex Singularities 2011, ed. Satoshi Koike, World Scientific Publishing Co. Pte Ltd, Singapore, pp. 75-86.
- Isaev, A V 2014, 'On two methods for reconstructing homogeneous hypersurface singularities from their Milnor algebras', Methods and Applications of Analysis, vol. 21, pp. 391-406.
- Huckleberry, A & Isaev, A 2013, 'On the Kobayashi hyperbolicity of certain tube domains', Proceedings of the American Mathematical Society, vol. 141, no. 9, pp. 3141-3146.
- Isaev, A 2013, 'Examples of application of nil-polynomials to the biholomorphic equivalence problem for isolated hypersurface singularities', Bulletin of the Institute of Mathematics, Academia Sinica (New Series), vol. 8, no. 2, pp. 193-217.
- Eastwood, M & Isaev, A 2013, 'Extracting invariants of isolated hypersurface singularities from their moduli algebras', Mathematische Annalen, vol. 356, pp. 73-98.
- Isaev, A & Zaitsev, D 2013, 'Reduction of five-dimensional uniformly Levi degenerate CR structures to absolute parallelisms', Journal of Geometric Analysis, vol. 23, pp. 1571-1605.
- Isaev, A 2013, 'On the classification of homogeneous hypersurfaces in complex space', International Journal of Mathematics, vol. 24, no. 8 (electronic only).
- Isaev, A 2012, 'Application of classical invariant theory to biholomorphic classification of plane curve singularities, and associated binary forms', Proceedings of the Steklov Institute of Mathematics, vol. 279, no. 1, pp. 245-256.
- Fels, G, Isaev, A, Kaup, W & Kruzhilin, N 2011, 'Isolated hypersurface singularities and special polynomial realizations of affine quadrics', Journal of Geometric Analysis, vol. 21, pp. 767-782.
- Isaev, A 2011, 'On the affine homogeneity of algebraic hypersurfaces arising from Gorenstein algebras', Asian Journal of Mathematics, vol. 15, pp. 631-640
- Isaev, A 2011, Spherical Tube Hypersurfaces, Springer, Heidelberg, Gemany.
- Isaev, A 2011, 'On the number of affine equivalence classes of spherical tube hypersurfaces', Mathematische Annalen, vol. 349, pp. 59-74.
- Isaev, A 2010, 'Simple elliptic hypersurface singularities: a new look at the equivalence problem', Japanese-Australian Workshop on Real and Complex Singularities 2009, ed. Toshizumi Fukui, Adam Harris, Alexander Isaev, Proceedings of the Centre for Mathematics and its Applications of the Australian National University, Canberra, vol. 43, pp. 9-17.
- Isaev, A & Kaup, W 2012, 'Regularization of local CR-automorphisms of real-analytic CR-manifolds', Journal of Geometric Analysis, vol. 22, no. 1 , pp. 244-260.
- Huckleberry, A & Isaev, A 2010, 'Classical symmetries of complex manifolds', Journal of Geometric Analysis, vol. 20, no. 1, pp. 132-152.
- Isaev, A & Kossovskiy, I 2010, 'Continuation of CR-automorphisms of Levi degenerate hyperquadrics to the projective space', Illinois Journal of Mathematics, vol. 54, pp. 747-752
- Huckleberry, A & Isaev, A 2009, 'Infinite-dimensionality of the automorphism groups of homogeneous Stein manifolds', Mathematische Annalen, vol. 344, pp. 279-291.
- Isaev, A & Kruzhilin, N 2009, 'Proper actions of Lie groups of dimension n^2+1 on n-dimensional complex manifolds', Israel Journal of Mathematics, vol. 172, pp. 193-252.
- Isaev, A 2009, 'Zero CR-curvature equations for rigid and tube hypersurfaces', Complex Variables and Elliptic Equations, vol. 54, no. 3-4, pp. 317-344.
- Isaev, A 2008, 'A Remark on a theorem by Kodama and Shimizu', Journal of Geometric Analysis, vol. 18, pp. 795-799.
- Isaev, A 2008, 'Complex manifolds admitting proper actions of high-dimensional groups', Journal of Lie Theory, vol. 18, pp. 141-160.
- Isaev, A 2008, 'Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism group', Geometry and Topology, vol. 12, pp. 643-711.
- Isaev, A 2008, 'On Chern-Moser normal forms of strongly pseudoconvex hypersurfaces with high-dimensional stability group', Pacific Journal of Mathematics, vol. 235, no. 2, pp. 235-244.
- Isaev, A 2008, 'On proper actions of Lie groups of dimension n^2+1 on n-dimensional complex manifolds', Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 1160-1174.
- Isaev, A 2007, Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds, Springer, Heidelberg, Gemany.
- Isaev, A 2007, 'Hyperbolic n-dimensional manifolds with automorphism group of dimension n^2', Geometric and Functional Analysis, vol. 2007, p. 28.
- Isaev, A 2007, 'Proper actions of high-dimensional groups on complex manifolds', Journal of Geometric Analysis, vol. 17, no. 4, pp. 649-667.
- Isaev, A & Kruzhilin, N 2006, 'Proper holomorphic maps between Reinhardt domains in C^2', Michigan Mathematics Journal, vol. 54, pp. 33-63.
- Isaev, A 2006, 'Analogues of Rossi's map and E. Cartan's classification of homogeneous strongly pseudoconvex 3-dimensional hypersurfaces', Journal of Lie Theory, vol. 16, pp. 407-426.
- Isaev, A 2006, 'Hyperbolic manifolds with high-dimensional automorphism group', Proceedings of the Steklov Institute of Mathematics, vol. 253, pp. 225-245.
- Eastwood, M & Isaev, A 2005, 'Examples of unbounded homogeneous domains in complex space', Science in China. Series A: Mathematics, vol. 48, pp. 248-261.
- Ezhov, V & Isaev, A 2005, 'On the dimension of the stability group for a Levi non-degenerate hypersurface', Illinois Journal of Mathematics, vol. 49, no. 4, pp. 1155-1169.
- Isaev, A 2005, 'Hyperbolic manifolds of dimension n with automorphism group of dimension n^2-1', Journal of Geometric Analysis, vol. 15, no. 2, pp. 239-259.
- Isaev, A 2005, 'On hyperbolic n-dimensional manifolds with automorphism group of dimension n^2', Complex Variables and Elliptic Equations, vol. 50, no. 5, pp. 345-355.
- Isaev, A 2004, Introduction to mathematical methods in bioinformatics, Springer, Berlin.
- Eastwood, M, Ezhov, V & Isaev, A 2004, 'Towards a classification of homogenous tube domains in C^4', Journal of Differential Geometry, vol. 68, pp. 553-569.
- Isaev, A & Kruzhilin, N 2004, 'Effective actions of SU_n on complex n-dimensional manifolds', Illinois Journal of Mathematics, vol. 48, pp. 37-57.
- Isaev, A 2004, 'Characterization of the unit ball in C^n among complex manifolds of dimension n', Journal of Geometric Analysis, vol. 4, pp. 697-700.
- Isaev, A 2003, 'Rotationally invariant complex manifolds', Journal of the Korean Mathematical Society, vol. 40, no. 3, pp. 391-408.
- Isaev, A & Kruzhilin, N 2002, 'Effective actions of the unitary group on complex manifolds', Canadian Journal of Mathematics, vol. 54, no. 6, pp. 1254-1279.
- Isaev, A & Krantz, S 2001, 'On the automorphism groups of hyperbolic manifolds', Journal fur die reine und angewandte Mathematik, vol. 534, pp. 187-194.
- Isaev, A 2001, 'Characterization of C^n by its automorphism group', Proceedings of the Steklov Institute of Mathematics, vol. 235, pp. 103-106.
- Gifford, J, Isaev, A & Krantz, S 2000, 'On the dimensions of the automorphosm groups of hyperbolic Reinhardt domains', Illinois Journal of Mathematics, vol. 44, pp. 602 - 618.
- Isaev, A & Krantz, S 2000, 'Characterization of Reinhardt domains by their automorphism groups', Journal of the Korean Mathematical Society, vol. 37, pp. 297 - 308.
- Isaev, A & Krantz, S 2000, 'Invariant distances and metrics in complex analysis', American Mathematical Society Notices, vol. 47, no. 5, pp. 546 - 553.
- Ezhov, V & Isaev, A 1999, 'Canonical isomorphism of two Lie algebras arising in CR-geometry', Publications of the Research Institute for Mathematical Sciences, vol. 35, no. 2, pp. 249-261.
- Ezhov, V, Isaev, A & Schmalz, G 1999, 'Invariants of elliptic and hyperbolic CR-structures of codimension 2', International Journal of Mathematics, vol. 10, no. 1, pp. 1-52.
- Isaev, A & Krantz, S 1999, 'Domains with non-compact automorphism group: a survey', Advances in Mathematics, vol. 146, pp. 1-38.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- The reconstruction and recognition problems for hypersurface singularities (Primary Investigator)
- Nilpotent Associative Algebras in Complex Geometry (Primary Investigator)