On the spectrum of cartan-hadamard manifolds

Mark A. Pinsky*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Let I be a simply-connected complete d-dimensional Riemannian manifold of nonpositive sectional curvature K.If K≦– k2<0, then the infimum of the L2spectrum of the negative Laplacian is greater than or equal to (d–1)2K2/4 with equality in case K⟶–k2sufficiently fast at infinity.This general result is obtained by analyzing a system of ordinary differential equations. If either d=2 or the manifold possesses appropriate symmetry, the result is obtained under weaker conditions by analyzing a Riccati equation.Finally the case k=0 is treated separately.

Original languageEnglish (US)
Pages (from-to)223-230
Number of pages8
JournalPacific Journal of Mathematics
Volume94
Issue number1
DOIs
StatePublished - May 1981

ASJC Scopus subject areas

  • Mathematics(all)

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