Sobolev inequalities in manifolds with nonnegative curvature

Abstract

We prove a sharp Sobolev inequality on manifolds with nonnegative Ricci curvature. Moreover, we prove a Michael-Simon inequality for submanifolds in manifolds with nonnegative sectional curvature. Both inequalities depend on the asymptotic volume ratio of the ambient manifold.

final version, to appear in Comm Pure Appl Math

Cited by in corpus (2)

• On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
• The isoperimetric problem via direct method in noncompact metric measure spaces with lower Ricci bounds