On plurisubharmonicity of the solution of the Fefferman equation and its applications to estimate the bottom of the spectrum of Laplace-Beltrami operators

Song-Ying Li

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arXiv · 1410.1577

On plurisubharmonicity of the solution of the Fefferman equation and its applications to estimate the bottom of the spectrum of Laplace-Beltrami operators

Song-Ying Li

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Abstract

In this paper, we introduce a concept of super-pseudoconvex domain. We prove that the solution of the Feffereman equation on a smoothly bounded strictly pseudoconvex domain $D$ in $\CC^n$ is plurisubharmonic if and only if $D$ is super-pseudoconvex. As an application, we give a lower bound estimate the bottom of the spectrum of Laplace-Beltrami operators when $D$ is super-pseudoconvex by using the result of Li and Wang \cite{LiWang}.

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Song-Ying Li. 2015-02-11. On plurisubharmonicity of the solution of the Fefferman equation and its applications to estimate the bottom of the spectrum of Laplace-Beltrami operators. https://arxiv.org/abs/1410.1577

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