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Papers of Vladimir Tkachev


    Nikolai Nadirashvili, Vladimir Tkachev, Serge G. Vlăduţ,
    Nonlinear Elliptic Equations and Nonassociative Algebras

    Vol.200, Mathematical Surveys and Monographs, AMS, 2014, 240 pp.

    See also selected chapters on the AMS website.

    Book on   Goggle Scholar,   zbMath

    See also Serge G. Vlăduţ presentation of the main results of the book

    in his talk on the conference "Algebraic Geometry and Number Theory", 2014, Moscow


  1. New explicit solutions to the p-Laplace equation based on isoparametric foliations, submitted, 2018,
    Available on [arXiv:1802.09892 ] ,  
  2. Algebraic cmc hypersurface of order 3 in Euclidean spaces, submitted to Pacific J. Math., 2018,
    Available on [arXiv:1802.04994] ,   (with Oscar Perdomo,)
  3. Global stability and persistence of complex foodwebs, submitted, 2017,
    Available on [arXiv:1712.02995 ] ,   (with Vladimir Kozlov, Sergey Vakulenko and Uno Wennergren)
  4. Permanency of the age-structured population model on several temporally variable patches, submitted, 2017,
    Available on [arXiv:1702.05979 ] ,   (with Vladimir Kozlov, Sonja Radosavljevic, and Uno Wennergren)


  5. Biodiversity and robustness of large ecosystems, Ecological Complexity, 36(2018), 101-109
    Available on [arXiv:1712.02995 ] ,   (with Vladimir Kozlov, Sergey Vakulenko and Uno Wennergren)
  6. Idempotent geometry in generic algebrass, to appear Adv. Appl. Clifford Algebr., 2018,
    Available on [arXiv:1802.04994] ,   (with Yakov Krasnov)
  7. On an extremal property of Jordan algebras of Clifford type, Comm. Algebra, to appear, 2018, Available on [arXiv:1802.04994] ,  
  8. Variety of idempotents in nonassociative algebras,
    Modern Trends in Hypercomplex Analysis, Trends Math. Birkhauser/Springer, 2018, to appear. Available on [arXiv:1801.00617] ,   (with Yakov Krasnov)
  9. Sharp pointwise gradient estimates for Riesz potentials with a bounded density, Anal. Math. Physics., 2018,
    Available on [arXiv:1803.11376] ,  
  10. New construction techniques for minimal surfaces,
    Complex Variables and Elliptic Equations, 2018, to appear [arXiv:1503.03234] ,   Goggle Scholar (with Jens Hoppe)
  11. A correction of the decomposability result in a paper by Meyer-Neutsch,
    Journal of Algebra, 2018, 504: 432-439 [arXiv:1503.03234] ,   Goggle Scholar
  12. Persistence analysis of the age-structured population model,
    CMMSE 2016. Universidad de Cádiz, 2016. Vol.3, 717-727. (with Vladimir Kozlov, Sonja Radosavljevic, and Uno Wennergren)
  13. On the non-vanishing property for real analytic solutions of the \(p\)-Laplace equation,
    Proc. Amer. Math. Soc., 2016, 144: 2375-2382 [arXiv:1503.03234] ,   Goggle Scholar
  14. A Jordan algebra approach to the eiconal equation,
    Journal of Algebra, 2014, 419:34-51 [arXiv:1211.7223] ,   Goggle Scholar

  15. A note on isoparametric polynomials,
    Analysis and Mathematical Physics, 2014, 4(3):237-245 [arXiv:1209.0155] ,   Goggle Scholar

  16. Non-classical solution to Hessian equation from Cartan isoparametric cubic   (with Nikolai Nadirashvili, Serge G. Vlăduţ ), Advances in Mathematics, 2012, 231(3/4):1589-1597 [arXiv:1211.7223] ,   Cited by 15

  17. On the exponential transform of multi-sheeted algebraic domains  (with B. Gustafsson),
    Computational Methods and Function Theory, 2011, 11(2):91-615 [arxiv:1101.0799] ,   Goggle Scholar

  18. On the exponential transform of lemniscates  (with B. Gustafsson),
    in Trends in Mathematics, Notions of Positivity and the Geometry of Polynomials (eds. P. Branden, M. Passare and M. Putinar), 2011, 239-257 [arxiv:1101.0794] ,   Goggle Scholar

  19. Minimal cubic cones via Clifford algebras,
    Complex Anal. and Operator Theory, 2010, 4(3): 685-700 [arxiv:1003.0215]   Goggle Scholar

  20. A generalization of Cartan's theorem on isoparametric cubics,
    Proc. Amer. Math. Soc., 2010, 138(8):2889-2895 [arxiv:1001.2387] ,   Goggle Scholar

  21. On the Jacobian of the harmonic moment map   (with B. Gustafsson),
    Complex Anal. and Operator Theory, 2009, 3(2):399-417 [arxiv:0903.3471] ,   Goggle Scholar

  22. Disjoint minimal graphs, Anal. Global Analysis and Geom., 2009, 35(2):139-155. [arxiv:0807.3694],   Goggle Scholar

  23. The resultant on compact Riemann surfaces   (with B. Gustafsson),
    Comm. Math. Physics 2009, 286:313-358, [arxiv:0710.2326]   Goggle Scholar

  24. Entire solutions of some quasilinear equations with quadratic principal symbol  (with Zorina I.G.),
    Vestnik SamGU, Matematika, 2008, 62(3), 108-123.   Goggle Scholar

  25. Positive definite collections of disks
    Indiana Univ. Math. J., 2006, 55(6):380-388. [arxiv:0709.4460]   Goggle Scholar

  26. Algebraic structure of quasiradial solutions to the \(\gamma\)-harmonic equation
    Pacific J. Math., 2006, 226(1):179-200, [arxiv:0709.4472]   Goggle Scholar

  27. Entire solutions of the Simon equation  (with Zorina I.G.),
    Geometric Analysis and applications, Proceedings, Volgograd, 2005, p. 55-74

  28. Subharmonicity of higher dimensional exponential transforms,
    Operator Theory: Advances and Appl., 2005, 156:257-277, [arxiv:0902.2742]   Goggle Scholar

  29. Ullemar formula for the moment map, II,
    Linear Algebra and Appl., 2005, 404: 380-388, [arxiv:0709.4275]   Goggle Scholar

  30. Ullemar's formula for the Jacobian of the complex moment mapping (with Kuznetsova O.S.),
    Complex Variables and Appl., 2004, 49:55-72, [arxiv:0306324]   Goggle Scholar

  31. Length functions on lemniscates , (with Kuznetsova O.S.)
    Manuscripta Math., 2003, 112(4):519-538, [arxiv:0306327]   Goggle Scholar

  32. Doubly periodic maximal surfaces with singularities (with Sergienko V.V.),
    Siberian Adv. Math. 2002, 12(1):77-91, [arxiv:0903.1368]   Goggle Scholar

  33. Unsolved problems in analysis
    Science Journal of Volgograd State University. Mathematics. Physics., 2002, 7:20-33. (in Russian)

  34. Radial symmetric solutions of the Hele-Shaw equation (with Mankaeva G.A.)
    Science Journal of Volgograd State University. Mathematics. Physics., 2001, 6:80-93. (in Russian)

  35. Some examples of \(p\)-minimal surfaces (with Yakhontov S.V.)
    Science Journal of Volgograd State University. Mathematics. Physics., 2001, 6:76-80. (in Russian)

  36. On the Gauss map of embedded minimal tubes (with Reshetninkova I.M),
    Note di Matematica 1999/2000, 19(1):7-17, [arxiv:0903.0228]   Goggle Scholar

  37. Entire one-periodic maximal surfaces (with Sergienko V.V.),
    The Mansfield-Volgograd Journal, Ed.: James York Glimm, Mansfield University of Pennsylvania, 2000. 148-156. [arxiv:0902.3810]   Goggle Scholar

  38. Asymptotic properties of solutions of the Hele-Shaw equation (with Kuznetsova O.S.),
    Dokl. Akad. Nauk, 1999, 367(2):164-165.   Goggle Scholar

  39. Minimal tubes of finite integral curvature
    Siberian Math. J., 1998, 39(1):159-167,   Goggle Scholar

  40. On the starlike minimal surfaces
    Science Journal of Volgograd State University. Mathematics. Physics., 1998, 3(1):52-58, DJVU   Goggle Scholar

  41. External geometry of p-minimal surfaces,
    Geometry from the Pacific Rim, Walter de Gruyter, Berlin, 1997, 363-375, [arxiv:0903.0176]   Goggle Scholar

  42. Denjoy-Ahlfors theorem for harmonic functions on Riemannian manifolds and external structure of minimal surfaces (with Miklyukov V.M.)
    Comm. Anal. Geom. 1996, 4(4):547-587, [arxiv:0903.2326] Cited by 18   Goggle Scholar

  43. On the bore radius for minimal surfaces
    Math. Notes 1996, 59(5-6):657-660,   Goggle Scholar

  44. On the gaussian image of minimal tubes with nondegenerate angle of flow-vector (with Reshetninkova I.M)
    Science Journal of Volgograd State University. Mathematics. Physics. 1996, 1(1):35-40,   Goggle Scholar

  45. Life-time of minimal tubes and coefficients of univalent functions in a circular ring,
    Bull. Soc. Sci. Lett. Lodz Ser. Rech. Deform. 1995, 20:19-26, , a scanned copy here   Goggle Scholar

  46. A remark on the Jorgens-Calabi-Pogorelov theorem
    Dokl. Akad. Nauk 1995, 340(3):317-318.   Goggle Scholar

  47. Finiteness of the number of ends of minimal submanifolds in Euclidean space
    Manuscr. Math., 1994, 82(3-4):313-330, [arxiv:0903.0169]   Goggle Scholar

  48. Some estimates for the mean curvature of nonparametric surfaces defined over domains in \(\mathbb{R}^n\),
    J. Math. Sci., 1994, 72(4):3250-3260,   Goggle Scholar

  49. A sharp lower bound for the first eigenvalue on a minimal surface,
    Math. Notes, 1993, 54(1-2):835-840,   Goggle Scholar

  50. Some estimates for the mean curvature of graphs over domains in \(\mathbb{R}^n\),
    Soviet Math. Dokl., 1991 42(2):387-390,   Goggle Scholar

  51. Some properties of tube minimal surfaces of arbitrary codimension (with Miklyukov V.M.),
    Math. USSR-Sb., 1991, 68(1):133-150,   Goggle Scholar

  52. The structure in the large of externally complete minimal surfaces in \(\mathbb{R}^3\) (with Miklyukov V.M.),
    Izv. Vyssh. Uchebn. Zaved. Mat., 1987, 7:30-36 (in English) (in Russian)   Goggle Scholar
  53. On a theorem of S.T. Yau and S.Y. Cheng, original (in Russian) and English translation here
    Proc. XXIId Conference "A Student and The Scientific Progress." , Novosibirsk, 1984, 66-68.

Conference Paper Abstracts

  1. Complex moments and starlike polynomials , Problems of Function Theory, Saratov, Saratov State Univeristy, 2002, 110-111 (with Kuznetsova O.S.)
  2. Two-periodic maximal surfaces with singularities, Proceedings on Analysis and Geometry, Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000, 571-584 (with Sergienko V.V.)
  3. Minimal surfaces of finite projective volume , Geometric analysis and its applications, Scientific schools of Volgograd State University. Ed: Miklyukov V.M., Volgograd, 1999, 369-410.
  4. Minimal hypersurfaces of finite projective volume , Geometrical Analsis: Scientific Scools of VolSU, Volgograd, 1999, 369-410.
  5. Upper estimates of volume growth for minimal quasigraphs , ICM 1998, Abstracts of short communications. Berlin, Aug. 18-27, 1998, 82-83.
  6. Starlike minimal hypersurfaces and Simon's problem, Trudy nauchn. konf., Volgograd, Iss. 4 , Volgograd, VolSU, 1996, 15-21.
  7. Starlike minimal hypersurfaces , Abstracts of Conference on Differential Geometry, Budapest, July 27-30, 1996. Budapest, 1996, p. 116.
  8. Minimal hypersurfaces which are graphs over spheres, In Geometry in large, Cherkassk State University, 11-16 September, 1995. p.36.
  9. Minimal submanifolds of finite projective volume, Trudy nauchn. konf., Volgograd, 5-9 December 1994, VolSU Ed., Volgograd, 1995, 23-29.
  10. The number of branches of the minimal submanifolds in Euclidean space , Proc. of ICM 94, Zurich, 1994, p.55.
  11. Estimates of exterior radius of elliptic hypersurfaces , Depon. VINITI, 1992, Manuscr. No 2031-B92, 17 p.
  12. Fuglede's theorem in Finsler space, In Potential Theory, Kiev, 1991, p. 19. (with Ushakov A.N.)   Goggle Scholar
  13. Minimal hypersurfaces in \(\mathbb{R}^n\) with finite multiplicity of spherical projection , Abstracts of Conference on Complex Analysis, Tashkent, 1989, p. 118.
  14. Interior and exterior structure of minimal submanifolds of arbitrary co-dimension , In Geometry and Analysis, Novosibirsk, Institute of Math., 1989, p. 109.
  15. On a sufficient condition of parabolicity for minimal surfaces with degenerating mean curvature vector , In Geometric function theory", Novosibirsk, Institute of Math., 1988, p. 101.
  16. On a sufficient condition of parabolicity , Abstracts of IXth Geometric Conference, Kishinev, 1988, p. 213.
  17. On one property of minimal bands , Abstracts of IXth Geometric Conference, Kishinev, 1988, p. 214. (with Miklyukov V.M.)
  18. On a sufficient condition of parabolicity of two-dimensional minimal surfaces in \(\mathbb{R}^n\) , In Geometry in large, Novosibirsk, Institute of Math., 1987, p. 119.
  19. On structure of complete minimal surfaces in \(\mathbb{R}^n\) , Abs. of Conference "Complex methods in Mathematical Physics", Donezk, 1984, 156-157 (with Miklyukov V.M.)

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Last updated: 2018-08-28