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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.

Authors :
ABOLARINWA, ABIMBOLA
ADEFOLARIN, ADEKUNLE
ANIMASAHUN, ISAAC A.
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]

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