Differential geometry.
Elliptic type PDEs.
Comlpex analysis.
Nonassociative algebras
Main publications:
Nadirashvili, N., and Tkachev, V.G. and Vlǎduţ, S., Nonlinear elliptic equations and nonassociative algebras, Mathematical Surveys and Monographs, 200, AMS, 2014
Tkachev V. G., “A Jordan algebra approach to the cubic eiconal equation”, J. of Algebra, 419 (2014), 34–51
Nadirashvili, N., and Tkachev, V.G. and Vlǎduţ, S., “A non-classical solution to a Hessian equation from Cartan isoparametric cubic”, Advances in Mathematics, 231:3-4 (2012), 1589–1597
Tkachev V. G., “Disjoint minimal graphs”, Annals of Global Analysis and Geometry, 35:2 (2009), 139–155
Gustafsson, Björn and Tkachev Vladimir G., “The resultant on compact Riemann surfaces”, Communications in Mathematical Physics, 286:1 (2009), 313–358
J. Andersson, S. Ghersheen, V. Kozlov, V. Tkachev, U. Wennergren, “Effect of density dependence on coinfection dynamics”, Anal. Math. Phys., 11:4 (2021), 1–28 (166)
J. Andersson, S. Ghersheen, V. Kozlov, V. Tkachev, U. Wennergren, “Effect of density dependence on coinfection dynamics: part 2”, Anal. Math. Phys., 11:4 (2021), 1–40 (169)
2020
4.
V.G. Tkachev, “New explicit solutions to the p-Laplace equation based on isoparametric foliations”, Differential Geom. Appl., 70 (2020), 18 (101629)
V. G. Tkachev, A. I. Ivanov, “The effect of asymmetric charge transfer on the IR spectra of excited quadrupolar molecules”, Optics and Spectroscopy, 128:11 (2020), 1707–1714
S. Ghersheen, V. Kozlov, V. Tkachev. U. Wennergren, “Mathematical analysis of complex SIR model with coinfection and density dependence”, Comp. Math. Meth., e1042:4 (2019), 1-17 , arXiv: 1905.04920
S. Ghersheen, V. Kozlov, V. Tkachev. U. Wennergren, “Dynamical behaviour of SIR model with coinfection: the case of finite carrying capacity”, Math. Meth. Appl. Sci., 42:17 (2019), 5805-5826 , arXiv: 1808.04846
Yakov Krasnov, Vladimir G. Tkachev, “Variety of Idempotents in Nonassociative Algebras”, Topics in Clifford Analysis, Special Volume in Honor of Wolfgang Sprößig, Trends in Mathematics, eds. Bernstein, Swanhild, Birkhäuser/Springer, 2019, 405-436
V. G. Tkachev, “V.M. Miklyukov: from dimension 8 to nonassociative algebras”, Mathematical Physics and Computer Simulation, 22:2 (2019), 33–50
14.
V. Kozlov, V.G. Tkachev, S. Vakulenko, U. Wennergren, “Global stability and persistence of complex foodwebs”, Ann. Mat. Pura Appl., 198:5 (2019), 1693–1709
V. G. Tkachev, “On the non-vanishing property for real analytic solutions of the $p$-Laplace equation”, Proc. Amer. Math. Soc., 144:6 (2016), 2375–2382 , arXiv: 1503.03234
N. Nadirashvili, V. Tkachev, S. Vlăduţ, Nonlinear elliptic equations and nonassociative algebras, Mathematical Surveys and Monographs, 200, American Mathematical Society, Providence, RI, 2014 , viii+240 pp.
F. G. Avkhadiev, V. A. Botvinnik, S. K. Vodop'yanov, M. Vuorinen, V. M. Gol'dstein, V. V. Goryainov, A. A. Grigor'yan, V. N. Dubinin, I. V. Zhuravlev, V. A. Zorich, V. M. Kesel'man, V. A. Klyachin, T. G. Latfullin, A. V. Loboda, A. G. Losev, O. Martio, V. I. Pelikh, S. I. Pinchuk, Yu. G. Reshetnyak, A. S. Romanov, A. G. Sergeev, V. G. Tkachev, E. M. Chirka, “Vladimir Mikhailovich Miklyukov (obituary)”, Russian Math. Surveys, 69:3 (2014), 565–568
2012
24.
N. Nadirashvili, V. Tkachev, S. Vlăduţ, “A non-classical solution to a Hessian equation from Cartan isoparametric cubic”, Adv. Math., 231:3-4 (2012), 1589–1597 , arXiv: 1111.0329
B. Gustafsson, V. Tkachev, “On the exponential transform of lemniscates”, Notions of positivity and the geometry of polynomials, Trends Math., Birkhäuser/Springer Basel AG, Basel, 2011, 239–257 , arXiv: 1101.0794
26.
B. Gustafsson, V. G. Tkachev, “On the exponential transform of multi-sheeted algebraic domains”, Comput. Methods Funct. Theory, 11:2 (2011), 591–615
I. A. Zorina, V. G. Tkachev, “O tselykh resheniyakh kvazilineinykh uravnenii s kvadratichnoi glavnoi chastyu”, Vestnik Samarskogo Gosudarstvennogo Universiteta, Ser. estestv. nauk., 2008, no. 3, 108–123Link to PDF
2006
34.
V. G. Tkachev, “Positive definite collections of disks”, Indiana Univ. Math. J., 55:6 (2006), 1907–1934 , arXiv: 0709.4460
35.
V. G. Tkachev, “Algebraic structure of quasiradial solutions to the $\gamma$-harmonic equation”, Pacific J. Math., 226:1 (2006), 179–200 , arXiv: 0709.4472
V. G. Tkachev, “Subharmonicity of higher dimensional exponential transforms”, Quadrature domains and their applications, Oper. Theory Adv. Appl., 156, Birkhäuser, Basel, 2005, 257–277 , arXiv: 0902.2742
O. S. Kuznetsova, V. G. Tkachev, “Ullemar's formula for the Jacobian of the complex moment mapping”, Complex Var. Theory Appl., 49:1 (2004), 55–72 , arXiv: 0306324
O.S. Kouznetsova, V. G. Tkachev, Analysis on lemniscates and Hamburger’s moments, Preprint TRITA-MAT-03-MA-04, Royal Institute of Technology, Stockholm, 2003 , 37 pp. Link to PDF
2002
41.
G.A. Mankaeva, V. G. Tkachev, “O logarifmicheskoi vypuklosti dliny lemniskaty”, Modeli i diskretnye struktury: Sb. nauch. tr. Elista, Dzhangar, 2002, 111-119
42.
V. G. Tkachev, “Positive trigonometric polynomials”, Tr. kaf. matem. analiza i teorii funktsii Volgogradskogo gosudarstvennogo universiteta, VolGU, Volgograd, 2002, 161-173Link to abstract and PDF
2001
43.
G.A. Mankaeva, V. G. Tkachev, “Radialno simmetricheskie resheniya uravneniya Khele-Shou”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika, 6:1 (2001), 80-93
44.
V. G. Tkachev, S.V. Yakhontov, “Primery p-minimalnykh poverkhnostei”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika, 6:1 (2001), 76-80
2002
45.
V. V. Sergienko, V. G. Tkachev, “Double periodic maximal surfaces with singularities”, Siberian Adv. Math., 12:1 (2002), 77–91 , arXiv: 0903.1368
2000
46.
V. V. Sergienko, V. G. Tkachev, “Entire one-periodic maximal surfaces”, The Mansfield-Volgograd Journal, eds. Ed.: James York Glimm, Mansfield University of Pennsylvania, 2000, 148-156arxiv: 0902.3810
1999
47.
I. M. Reshetnikova, V. G. Tkachev, “On the Gauss map of embedded minimal tubes”, Note Mat., 19:1 (1999), 7–17 (2000)Link to PDF, arXiv: 0903.0228
48.
O. S. Kuznetsova, V. G. Tkachev, “Asymptotic properties of solutions of the Hele-Shaw equation”, Dokl. Akad. Nauk, 367:2 (1999), 164–165Link to PDF
1998
49.
V. G. Tkachev, “Minimal tubes of finite integral curvature”, Siberian Math. J., 39:1 (1998), 159–167
50.
V. G. Tkachev, “Zvezdnye minimalnye poverkhnosti”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika., 3:1 (1998), 52-58Link to abstract and PDF
1996
51.
V. G. Tkachev, “On the bore radius for minimal surfaces”, Math. Notes, 59:6 (1996), 657–660
52.
V. Miklyukov, V. Tkachev, “Denjoy-Ahlfors theorem for harmonic functions on Riemannian manifolds and external structure of minimal surfaces”, Comm. Anal. Geom., 4:4 (1996), 547–587 , arXiv: 0903.2326
I. M. Reshetnikova, V. G. Tkachev, “O gaussovom obraze minimalnykh trubok s nenulevym uglom vektora potoka”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika., 1:1 (1996), 35-40Link to abstract and PDF
1995
54.
V. G. Tkachev, “Life-time of minimal tubes and coefficients of univalent functions in a circular ring”, Bull. Soc. Sci. Lett. Łódź Sér. Rech. Déform., 20 (1995), 19–26
55.
V. G. Tkachev, “A remark on the Jörgens-Calabi-Pogorelov theorem”, Dokl. Akad. Nauk, 340:3 (1995), 317–318Link to PDF, arXiv: 1311.1498
1994
56.
V. G. Tkachev, “Finiteness of the number of ends of minimal submanifolds in Euclidean space”, Manuscripta Math., 82:3-4 (1994), 313–330
V. G. Tkachev, “A sharp lower bound for the first eigenvalue on a minimal surface”, Math. Notes, 54:2 (1993), 835–840
1992
58.
V. G. Tkachev, “Some estimates for the mean curvature of nonparametric surfaces defined over domains in $\mathbb{R}^n$”, Ukrain. Geom. Sb., 1992, no. 35, 135–150, 166Link to PDF
V. G. Tkachev, “Some estimates for the mean curvature of graphs over domains in $\mathbb{R}^n$”, Soviet Math. Dokl., 42:2 (1991), 387–390Link to PDF; V. G. Tkachev, “Nekotorye otsenki srednei krivizny grafikov nad oblastyami v Rn”, Doklady AN SSSR, 314:1 (1990), 140-143 (to appear)
60.
V. G. Tkachev. A.N. Ushakov, “Teorema Fuglede v finslerovom prostranstve”, Tez. dokl. Vsesoyuzn. shkoly “Teoriya potentsiala” (Kiev, 1991), IM AN USSR, 1991, 19
61.
V. M. Miklyukov, V. G. Tkachev, “Some properties of the tubular minimal surfaces of arbitrary codimension”, Math. USSR-Sb., 68:1 (1991), 133–150
1987
62.
V. M. Miklyukov, V. G. Tkachev, “The structure in the large of externally complete minimal surfaces in $\mathbb{R}^3$”, Soviet Math. (Iz. VUZ), 31:7 (1987), 37–45Link to PDF
1984
63.
V. G. Tkachev, “Ob odnoi teoreme Chenga i Yao”, Materialy XXII Vsesoyuznoi nauchnoi studencheskoi konferentsii “Student i NTP” (Novosibirsk, mai 1984), NGU, 1984, 66-68Link to PDF
2021
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