On the eigenvalue counting function for weighted Laplace-Beltrami operators
type: Item
instance of: scholarly article
title: On the eigenvalue counting function for weighted Laplace-Beltrami operators
zbMATH Open document ID: 0982.58021
DOI: 10.1007/BF02921827
author: M. Lianantonakis
published in: The Journal of Geometric Analysis
publication date: 2000-12-11T00:00:00Z
review text: It is well known that a weighted Laplace Beltrami operator on a Riemannian manifold \( M \) is an operator of the form: \[ H = - \overline{\sigma} ^2 \nabla (\sigma \nabla), \] where \( \sigma \) is a positive, locally bounded function defined on \( M \). In the paper under review the author obtains some upper and lower bounds on the eigenvalue counting function of \( H \) for a class of incomplete manifolds with locally bounded geometry and for certain weights \( \sigma \).
reviewed by: Mircea Puta
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 1542076
zbMATH Keywords: eigenvalue counting function
zbMATH Keywords: weighted Laplace operators
zbMATH Keywords: spectrum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1542076