# A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds

## TL;DR

This paper derives Willmore-type inequalities for hypersurfaces in non-compact Riemannian manifolds with specific Ricci curvature bounds, extending recent results and providing new geometric inequalities.

## Contribution

It introduces new Willmore-type inequalities under asymptotic or integral Ricci curvature conditions, generalizing previous inequalities in the field.

## Key findings

- Established Willmore-type inequalities for hypersurfaces
- Extended recent inequality results to broader curvature bounds
- Provided geometric bounds applicable to non-compact manifolds

## Abstract

We establish Willmore-type inequalities for bounded domains in complete non-compact Riemannian manifolds, under either asymptotic or integral Ricci curvature bounds. Those results recover a recent inequality of Jin-Yin arXiv:2402.02465.