LOGARITHMIC SOBOLEV INEQUALITIES ON NONCOMPACT RIEMANNIAN-MANIFOLDS

Authors
WANG FY
Citation
Fy. Wang, LOGARITHMIC SOBOLEV INEQUALITIES ON NONCOMPACT RIEMANNIAN-MANIFOLDS, Probability theory and related fields, 109(3), 1997, pp. 417-424
Citations number
15
Journal title
Probability theory and related fields → ACNP
ISSN journal
01788051
Volume
109
Issue
3
Year of publication
1997
Pages
417 - 424
Database
ISI
SICI code
0178-8051(1997)109:3<417:LSIONR>2.0.ZU;2-J
Abstract
This paper presents a dimension-free Harnack type inequality for heat semigroups on manifolds, from which a dimension-free lower bound is ob tained for the logarithmic Sobolev constant on compact manifolds and a new criterion is proved for the logarithmic Sobolev inequalities (abb rev. LSI) on noncompact manifolds. As a result, it is shown that LSI m ay hold even though the curvature of the operator is negative everywhe re.