Some characterizations of compact Einstein-type manifolds

TL;DR

This paper explores the geometric and topological properties of compact Einstein-type manifolds with boundary, providing boundary estimates, topological classifications, and gap results to deepen understanding of their structure.

Contribution

It introduces new boundary estimates, a topological classification of boundaries, and a gap theorem for compact Einstein-type manifolds with boundary.

Findings

Sharp boundary estimate established

Hawking mass bounded from below under certain conditions

Topological classification of boundary components

Abstract

In this work, we investigate the geometry and topology of compact Einstein-type manifolds with nonempty boundary. First, we prove a sharp boundary estimate, as consequence we obtain under certain hypotheses that the Hawking mass is bounded from bellow in terms of area. Then we give a topological classification for its boundary. Finally, we prove a gap result for a compact Einstein-type manifold with boundary.