A logarithmic Sobolev inequality for closed submanifolds with constant length of mean curvature vector

TL;DR

This paper establishes a logarithmic Sobolev inequality for closed submanifolds with constant mean curvature length within manifolds of nonnegative sectional curvature, advancing geometric analysis tools.

Contribution

It introduces a new logarithmic Sobolev inequality applicable to a specific class of submanifolds in curved ambient spaces.

Findings

Proves a logarithmic Sobolev inequality for these submanifolds.

Applicable in manifolds with nonnegative sectional curvature.

Enhances understanding of geometric inequalities in submanifold theory.

Abstract

In this paper, we prove a logarithmic Sobolev inequality for closed submanifolds with constant length of mean curvature vector in a manifold with nonnegative sectional curvature.