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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 VIDEO presentation of the main results of the book

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


    Available on [arXiv:1802.09892 ] ,  
  1. 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)



  2. Effect of density dependence on coinfection dynamics. Anal.Math.Phys. 11, 166 (2021). with Andersson, J., Ghersheen, S., Kozlov, U. Wennergren
  3. The universality of one half in commutative nonassociative algebras with identities, J. Algebra, 569(2021), 466-510


  4. New explicit solutions to the p-Laplace equation based on isoparametric foliations, Diff. Geom. and Applic., 2020, 70, 101629


  5. Dynamical behaviour of SIR model with coinfection: the case of finite carrying capacity, Math. Methods in Appl. Sci., 42 (2019), no. 17, 5805–5826, see doi ,   (with Samia Ghersheen, Vladimir Kozlov, and Uno Wennergren)
  6. Mathematical analysis of SIR models with a complex coinfection and density dependence, Computational and Mathematical Methods, 1(2019), no. 4, e1042. (with Samia Ghersheen, Vladimir Kozlov, and Uno Wennergren) ,  
  7. V.M. Miklyukov: from dimension 8 to nonassociative algebras , Math. Phys. Comp. Simul. 2019, to appear
  8. Global stability and persistence of complex foodwebs, Ann. Mat. Pur. Appl., 2019, DOI,  Available on [arXiv:1712.02995 ] (with Vladimir Kozlov, Sergey Vakulenko and Uno Wennergren)
  9. Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs, Algebra i Analiz, 31(2019), no. 2, 51-74, see also St. Petersburg Math. J.
  10. Algebraic cmc hypersurface of order 3 in Euclidean spaces, J. Geometry, 110(2019), no. 1, 110:6 Available on [arXiv:1706.05093] ,   (with Oscar Perdomo)
  11. On an extremal property of Jordan algebras of Clifford type, Comm. Algebra, 47(2019), no.3, 1057-1066 Available on [arXiv:1802.04994] ,  
  12. 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)
  13. New construction techniques for minimal surfaces, Complex Variables and Elliptic Equations, 2018, to appear [arXiv:1503.03234] ,   Goggle Scholar (with Jens Hoppe)


  14. 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)
  15. Idempotent geometry in generic algebrass, Adv. Appl. Clifford Algebr., 2018, 28:84 Available on [arXiv:1802.04994] ,   (with Yakov Krasnov)
  16. Sharp pointwise gradient estimates for Riesz potentials with a bounded density, Anal. Math. Physics., 2018, Available on [arXiv:1803.11376] ,  
  17. A correction of the decomposability result in a paper by Meyer-Neutsch, Journal of Algebra, 2018, 504: 432-439 [arXiv:1503.03234] ,   Goggle Scholar


  18. 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)
  19. 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


  20. A Jordan algebra approach to the eiconal equation, Journal of Algebra, 2014, 419:34-51 [arXiv:1211.7223] ,   Goggle Scholar

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


  22. 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] ,   Google


  23. 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

  24. 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


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

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

    Before 2010

  27. 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

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

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

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

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

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

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

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

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

  36. 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

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

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

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

  40. 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)

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

  42. 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

  43. 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

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

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

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

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

  48. 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

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

  50. 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

  51. 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

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

  53. 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

  54. 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

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

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

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

  58. 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  
  59. 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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