On Stekloff eigenvalue problem
type: Item
instance of: scholarly article
title: On Stekloff eigenvalue problem
zbMATH Open document ID: 1015.58010
author: Roger Chen
author: Chiung-Jue Sung
published in: Pacific Journal of Mathematics
publication date: 2000-12-03T00:00:00Z
review text: A smooth manifold \(M^n\) with boundary \(\partial M^n\) satisfies the ``interior rolling \(R\)-ball'' condition if every \(q\in\partial M^n\) is the only common point of a boundary and some closed metric ball in \(M^n\) of radius \(R\). In this paper the authors consider the Stekloff eigenvalue problem (i.e., \((-\Delta+q)u(x)=0\) on \(M^n\) and \(\partial u/ \partial\nu=\lambda u\) on \(\partial M^n\) for some \(C^2\) function \(q\)) and obtain a positive lower bound for the first nonzero eigenvalue in terms of \(n\), the diameter of \(M^n\), \(R\), the lower bound of the Ricci curvature, the lower bound of the second fundamental form elements, and the tangential derivatives of the second fundamental form elements.
reviewed by: Valery Borisovich Marenich
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J32
zbMATH DE Number: 1537865
zbMATH Keywords: Stekloff eigenvalue problem
zbMATH Keywords: Ricci curvature
zbMATH Keywords: second fundamental form
zbMATH Keywords: tangential derivatives
MaRDI profile type: Publication
OpenAlex ID: W2036109139
DOI: 10.2140/PJM.2000.195.277
description: scientific article; zbMATH DE number 1537865