Abstract:
In this paper we study the behavior of bounded harmonic functions on complete Riemannian manifolds (of a certain special type) depending on the geometry of the manifold.
Citation:
A. G. Losev, “On the hyperbolicity criterion for noncompact Riemannian manifolds of special type”, Mat. Zametki, 59:4 (1996), 558–564; Math. Notes, 59:4 (1996), 400–404
\Bibitem{Los96}
\by A.~G.~Losev
\paper On the hyperbolicity criterion for noncompact Riemannian manifolds of special type
\jour Mat. Zametki
\yr 1996
\vol 59
\issue 4
\pages 558--564
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\crossref{https://doi.org/10.4213/mzm1750}
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\transl
\jour Math. Notes
\yr 1996
\vol 59
\issue 4
\pages 400--404
\crossref{https://doi.org/10.1007/BF02308689}
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Linking options:
https://www.mathnet.ru/eng/mzm1750
https://doi.org/10.4213/mzm1750
https://www.mathnet.ru/eng/mzm/v59/i4/p558
This publication is cited in the following 11 articles:
A. G. Losev, E. A. Mazepa, “Asymptotic behavior of solutions of the Dirichlet problem for the Poisson equation on model Riemannian manifolds”, Sib. elektron. matem. izv., 19:1 (2022), 66–80
Mazepa E.A., “Solvability of Boundary Value Problems For Poisson'S Equation in Unbounded Domains on Noncompact Riemannian Manifolds”, Differ. Equ., 56:3 (2020), 324–329
Losev A., Mazepa E., Romanova I., “Eigenfunctions of the Laplace Operator and Harmonic Functions on Model Riemannian Manifolds”, Lobachevskii J. Math., 41:11, SI (2020), 2190–2197
A. N. Kondrashov, “On the asymptotics of solutions of elliptic equations at the ends
of non-compact Riemannian manifolds with metrics of a special form”, Izv. Math., 83:2 (2019), 287–314
Losev A.G., “Solvability of the Dirichlet Problem For the Poisson Equation on Some Noncompact Riemannian Manifolds”, Differ. Equ., 53:12 (2017), 1595–1604
Korol'kov S.A., “on the Solvability of Boundary Value Problems For the Stationary Schrodinger Equation in Unbounded Domains on Riemannian Manifolds”, Differ. Equ., 51:6 (2015), 738–744
S. A. Korolkov, “O vzaimosvyazi razreshimostei nekotorykh
kraevykh zadach dlya L-garmonicheskikh funktsii v neogranichennykh
oblastyakh rimanovykh mnogoobrazii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 2(21), 17–26
Yu. V. Goncharov, A. G. Losev, A. V. Svetlov, “Garmonicheskie funktsii na konusakh modelnykh mnogoobrazii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 3(22), 13–22
E. A. Mazepa, “Boundary value problems and Liouville theorems for semilinear elliptic equations on Riemannian manifolds”, Russian Math. (Iz. VUZ), 49:3 (2005), 56–62
Losev, AG, “Bounded solutions of Shrodinger equation on noncompact reimannian manifolds of special type”, Doklady Akademii Nauk, 367:2 (1999), 166
A.G. Losev, “Elliptic partial differential equations on the warped products of riemannian manifolds”, Applicable Analysis, 71:1-4 (1998), 325