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
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
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.
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
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
V. M. Miklyukov, V. G. Tkachev, “Some properties of the tubular minimal surfaces of arbitrary codimension”, Math. USSR-Sb., 68:1 (1991), 133–150
12.
St. Petersburg Math. J., 31:2 (2019), 223–240
13.
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
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
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
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
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
Vladimir G. Tkachev, “On an extremal property of Jordan algebras of Clifford type”, Communications in Algebra, 47:3 (2019), 1057-1066 https://www.tandfonline.com/doi/full/10.1080/00927872.2018.1499924, arXiv: arxiv:1801.05724
V. G. Tkachev, “V.M. Miklyukov: from dimension 8 to nonassociative algebras”, Mathematical Physics and Computer Simulation, 22:2 (2019), 33–50
28.
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
Vladimir G. Tkachev, “Sharp pointwise gradient estimates for Riesz potentials with a bounded density”, Analysis and Mathematical Physics, 8:2 (2018), 1-20 (Published online) https://link-springer-com.e.bibl.liu.se/article/10.1007, arXiv: https://arxiv.org/abs/1803.11376
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, “Minimal tubes of finite integral curvature”, Siberian Math. J., 39:1 (1998), 159–167
33.
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. 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
35.
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)
Jens Hoppe, Vladimir G. Tkachev, “New construction techniques for minimal surfaces”, Complex Variables and Elliptic Equations, 63 (2019) (to appear) https://www.tandfonline.com/doi/full/10.1080/17476933.2018.1542688, arXiv: 1708.05397
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
V. G. Tkachev, “On the bore radius for minimal surfaces”, Math. Notes, 59:6 (1996), 657–660
41.
V. G. Tkachev, “A sharp lower bound for the first eigenvalue on a minimal surface”, Math. Notes, 54:2 (1993), 835–840
42.
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)
43.
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
44.
V. G. Tkachev, Non-isoparametric solutions of the eikonal equation, 2010 (Published online) , 12 pp., arXiv: 1009.1842
45.
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
46.
V. G. Tkachev, “Positive definite collections of disks”, Indiana Univ. Math. J., 55:6 (2006), 1907–1934 , arXiv: 0709.4460
47.
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
48.
G.A. Mankaeva, V. G. Tkachev, “O logarifmicheskoi vypuklosti dliny lemniskaty”, Modeli i diskretnye struktury: Sb. nauch. tr. Elista, Dzhangar, 2002, 111-119
49.
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
50.
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
51.
V. G. Tkachev, S.V. Yakhontov, “Primery p-minimalnykh poverkhnostei”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika, 6:1 (2001), 76-80
52.
V. V. Sergienko, V. G. Tkachev, “Double periodic maximal surfaces with singularities”, Siberian Adv. Math., 12:1 (2002), 77–91 , arXiv: 0903.1368
53.
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
54.
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
55.
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
56.
V. G. Tkachev, “Zvezdnye minimalnye poverkhnosti”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika., 3:1 (1998), 52-58Link to abstract and PDF
57.
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
58.
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
59.
V. G. Tkachev, “A remark on the Jörgens-Calabi-Pogorelov theorem”, Dokl. Akad. Nauk, 340:3 (1995), 317–318Link to PDF, arXiv: 1311.1498
60.
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)
61.
V. G. Tkachev. A.N. Ushakov, “Teorema Fuglede v finslerovom prostranstve”, Tez. dokl. Vsesoyuzn. shkoly “Teoriya potentsiala” (Kiev, 1991), IM AN USSR, 1991, 19
62.
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
63.
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