paper

Sobolev inequalities involving 2-tensor fields in manifolds with nonnegative sectional curvature

arXiv:2409.14529

Abstract

By applying the ABP method, we establish both Log Sobolev type inequality and Michael Simon Sobolev inequality for smooth symmetric uniformly positive definite (0,2) tensor fields in manifolds with nonnegative sectional curvature.

14 pages

Sobolev inequalities involving 2-tensor fields in manifolds with nonnegative sectional curvature · wovepaper