On manifolds with non-negative Ricci curvature and Sobolev inequalities

Authors
Ledoux, M
Citation
M. Ledoux, On manifolds with non-negative Ricci curvature and Sobolev inequalities, COMMUN AN G, 7(2), 1999, pp. 347-353
Citations number
11
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ANALYSIS AND GEOMETRY
ISSN journal
10198385 → ACNP
Volume
7
Issue
2
Year of publication
1999
Pages
347 - 353
Database
ISI
SICI code
1019-8385(199904)7:2<347:OMWNRC>2.0.ZU;2-8
Abstract
Let M be a complete n-dimensional Riemanian manifold with nonnegative Ricci curvature in which one of the Sobolev inequalities (integral \ f \(p) dv) (1/p) less than or equal to C (integral \del f \(q) dv) (1/q), f epsilon C- 0(infinity) (M), 1 less than or equal to q < n, 1/p = 1/q - 1/n, is satisfi ed with C the optimal constant of this inequality in R-n. Then M is isometr ic to R-n.