Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Kokarev, Gerasim"'
Autor:
Kokarev, Gerasim
We compute the Laplacian spectra of singular area-minimising hypersurfaces in the hyperbolic space with prescribed asymptotic data. We also obtain similar results in higher codimension, and explore related extremal properties of the bottom of the spe
Externí odkaz:
http://arxiv.org/abs/2312.02947
We consider Calderon's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry
Externí odkaz:
http://arxiv.org/abs/2112.13419
Autor:
Kokarev, Gerasim
We obtain inequalities for all Laplace eigenvalues of Riemannian manifolds with an upper sectional curvature bound, whose rudiment version for the first Laplace eigenvalue was discovered by Berger in 1979. We show that our inequalities continue to ho
Externí odkaz:
http://arxiv.org/abs/1910.06647
Autor:
Kokarev, Gerasim
We prove inequalities for Laplace eigenvalues of Kaehler manifolds generalising to higher eigenvalues the classical inequality for the first Laplace eigenvalue due to Bourguignon, Li, and Yau in 1994. We also obtain similar inequalities for analytic
Externí odkaz:
http://arxiv.org/abs/1801.02276
Autor:
Kokarev, Gerasim
We prove inequalities for Laplace eigenvalues on Riemannian manifolds generalising to higher eigenvalues two classical inequalities for the first Laplace eigenvalue - the inequality in terms of the $L^2$-norm of mean curvature, due to Reilly in 1977,
Externí odkaz:
http://arxiv.org/abs/1712.08150
Autor:
Kokarev, Gerasim
Publikováno v:
Indiana University Mathematics Journal, 2020 Jan 01. 69(6), 1975-2003.
Externí odkaz:
https://www.jstor.org/stable/26959881
We revisit classical eigenvalue inequalities due to Buser, Cheng, and Gromov on closed Riemannian manifolds, and prove the versions of these results for the Dirichlet and Neumann boundary value problems. Eigenvalue multiplicity bounds and related ope
Externí odkaz:
http://arxiv.org/abs/1510.07281
We study Laplace eigenvalues $\lambda_k$ on K\"ahler manifolds as functionals on the space of K\"ahler metrics with cohomologous K\"ahler forms. We introduce a natural notion of a $\lambda_k$-extremal K\"ahler metric and obtain necessary and sufficie
Externí odkaz:
http://arxiv.org/abs/1411.7725
Autor:
Kokarev, Gerasim
Publikováno v:
In Advances in Mathematics 13 May 2020 365
Akademický článek
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