Warped area-minimizing hypersurface and warped product metric

TL;DR

This paper investigates warped area-minimizing hypersurfaces and demonstrates that under certain spectral curvature bounds, the metric can be locally expressed as a warped product, revealing structural geometric properties.

Contribution

The paper establishes a new link between spectral curvature bounds and the local warped product structure of metrics in the context of area-minimizing hypersurfaces.

Findings

Metrics can be locally split as warped products under spectral Ricci bounds.

Spectral scalar curvature bounds imply local warped product structure.

Provides new insights into geometric analysis of hypersurfaces.

Abstract

By studying the warped(or weighted) area-minimizing hypersurface, we prove that the metric can be locally split as a warped product metric under the spectral Ricci or spectral scalar curvature lower bound condition.