Which Ambient Spaces Admit Isoperimetric Inequalities for Submanifolds?

TL;DR

This paper establishes clear and straightforward conditions on ambient manifolds that are both necessary and sufficient for the validity of isoperimetric inequalities for submanifolds, advancing understanding in geometric analysis.

Contribution

It provides simple, precise criteria characterizing when isoperimetric inequalities hold for submanifolds within ambient spaces.

Findings

Identifies necessary and sufficient conditions for isoperimetric inequalities.

Simplifies understanding of ambient space properties affecting inequalities.

Contributes to geometric analysis and submanifold theory.

Abstract

We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.