Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces

TL;DR

This paper establishes Sobolev and isoperimetric inequalities for submanifolds within weighted manifolds, extending classical inequalities to more general weighted ambient spaces.

Contribution

It generalizes Hoffman-Spruck's inequalities to submanifolds in weighted ambient spaces, broadening the scope of geometric inequalities.

Findings

Proved Sobolev inequalities for submanifolds in weighted manifolds.

Established isoperimetric inequalities in the same setting.

Extended classical inequalities to weighted ambient spaces.

Abstract

In this paper, we prove a Sobolev and isoperimetric inequalities for submanifold in weighted manifold. Our results generalize the Hoffman-Spruck's inequalities.