紧流形上的Schrödinger算子的谱间隙估计

Abstract

Abstract:

Let $M$ be an $n$ -dimensional compact Riemannian manifold with strictly convex boundary. Suppose that the Ricci curvature of $M$ is bounded below by $(n-1)K$ for some constant $K\geq0$ and the first eigenfunction $f_1$ of Dirichlet (or Robin) eigenvalue problem of a Schrödinger operator on $M$ is log-concave. Then we obtain a lower bound estimate of the gap between the first two Dirichlet (or Robin) eigenvalues of such Schrödinger operator. This generalizes a recent result by Andrews et al. ([4]) for Laplace operator on a bounded convex domain in $\mathbb{R} ^n$ .

Key words: Schrödinger operator, Dirichlet eigenvalue, Robin eigenvalue, Spectral gap, Manifold with convex boundary, Ricci curvature

CLC Number:

O186.1

Yue He,Hailong Her. An Estimate of Spectral Gap for Schrödinger Operators on Compact Manifolds[J].Acta mathematica scientia,Series A, 2020, 40(2): 257-270.

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	He Yue . New estimates of lower bound for the first eigenvalue on compact manifolds with positive Ricci curvature. Acta Math Sci, 2016, 36A (2): 215- 230 doi: 10.3969/j.issn.1003-3998.2016.02.002

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An Estimate of Spectral Gap for Schrödinger Operators on Compact Manifolds

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