Sharp upper bound for the first non-zero Neumann eigenvalue for bounded domains in rank-1 symmetric spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Sharp upper bound for the first non-zero Neumann eigenvalue for bounded domains in rank-1 symmetric spaces

Authors:	A R Aithal G Santhanam

Institution:	Department of Mathematics, University of Bombay, Vidyanagare, Bombay-400098, India ; School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400-005, India

Abstract:	In this paper, we prove that for a bounded domain $\Omega$ in a rank- symmetric space, the first non-zero Neumann eigenvalue $\mu _{1}(\Omega )\leq \mu _{1}(B(r_{1}))$ where $B(r_{1})$ denotes the geodesic ball of radius $r_{1}$ such that $\begin{equation}vol(\Omega )=vol(B(r_{1}))\end{equation}$ and equality holds iff $\Omega =B(r_{1})$ . This result generalises the works of Szego, Weinberger and Ashbaugh-Benguria for bounded domains in the spaces of constant curvature.

Keywords:	Eigenvalue centre of mass Riemannian submersion

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