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SOBOLEV-TYPE INEQUALITIES AND COMPLETE RIEMANNIAN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE.
SOBOLEV-TYPE INEQUALITIES AND COMPLETE RIEMANNIAN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE.
- Source :
-
Bulletin of Mathematical Analysis & Applications . 2019, Vol. 11 Issue 1, p11-21. 11p. - Publication Year :
- 2019
-
Abstract
- Let M be an n-dimensional complete Riemannian manifold, we investigate the geometric nature of such M which admits any of the family of Sobolev-type inequalities with the optimal Euclidean Sobolev constant. This leads to several conditions under which M with nonnegative Ricci curvature is isometric to Euclidean space ℤn. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CURVATURE
*RIEMANNIAN manifolds
*MATHEMATICAL equivalence
Subjects
Details
- Language :
- English
- ISSN :
- 18211291
- Volume :
- 11
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Bulletin of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 136359974