Characterizations of the compactness of Riemannian manifolds by eigenfunctions, and a partial proof of a conjecture by Hamilton
type: Item
instance of: scholarly article
title: Characterizations of the compactness of Riemannian manifolds by eigenfunctions, and a partial proof of a conjecture by Hamilton
zbMATH Open document ID: 1345.35065
DOI: 10.1216/RMJ-2016-46-2-461
author: Xiang Gao
published in: Rocky Mountain Journal of Mathematics
publication date: 2016-09-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1469537473
review text: The author establishes comparison theorems related to the first eigenvalue of the Schrödinger operator. On the basis of these results, characterizations of Ricci solitons as space forms are obtained. Partial answer to a conjecture formulated by Hamilton is given.
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 6624470
zbMATH Keywords: Laplacian operator
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: eigenvalue
zbMATH Keywords: Dirichlet eigenvalue
zbMATH Keywords: eigenfunction
Wikidata QID: Q115240032
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6624470