紧流形上的Schrodinger算子的谱间隙估计 |
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引用本文: | 何跃,赫海龙.紧流形上的Schrodinger算子的谱间隙估计[J].数学物理学报(A辑),2020(2):257-270. |
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作者姓名: | 何跃 赫海龙 |
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作者单位: | 南京师范大学数学科学学院数学研究所;暨南大学数学系 |
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基金项目: | 国家自然科学基金(11671209,11871278);江苏高校优势学科建设工程资助项目。 |
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摘 要: | M是一个n维紧黎曼流形,具有严格凸边界,且Ricci曲率不小于(n-1)K(其中K≥0为某个常数).假定Schrodinger算子的Dirichlet (或Robin)特征值问题的第一特征函数f1在M上是对数凹的,该文得到了此类Schrodinger算子的前两个Dirichlet(或Robin)特征值之差的下界估计,这推广了最近Andrews等人在R^n中有界凸区域上关于Laplace算子的一个相应结果4].
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关 键 词: | SchrSodinger算子 Dirichlet特征值 Robin特征值 谱间隙 具有凸边界的流形 RICCI曲率 |
An Estimate of Spectral Gap for Schrodinger Operators on Compact Manifolds |
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Institution: | (Institute of Mathematics,School of Mathematics Sciences,Nanjing Normal University,Nanjing 210023;Department of Mathematics,Jinan University,Guangzhou 510632) |
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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≥0 and the first eigenfunction f1 of Dirichlet(or Robin)eigenvalue problem of a Schrodinger 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 Schrodinger operator.This generalizes a recent result by Andrews et al.(4])for Laplace operator on a bounded convex domain in R^n. |
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Keywords: | Schrodinger operator Dirichlet eigenvalue Robin eigenvalue Spectral gap Manifold with convex boundary Ricci curvature |
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