Geometry of Einstein-type manifolds with boundary

TL;DR

This paper explores Einstein-type manifolds with boundary, generalizing key geometric equations, and establishes boundary estimates related to eigenvalues and mass concepts, contributing to geometric analysis.

Contribution

It introduces new geometric inequalities and boundary estimates for Einstein-type manifolds with boundary, extending existing theories to broader classes of manifolds.

Findings

Derived geometric inequalities for Einstein-type manifolds with boundary.

Established boundary estimates involving the first eigenvalue of the Jacobi operator.

Connected boundary estimates to the Brown-York mass concept.

Abstract

In this article, we consider Einstein-type manifolds with boundary which generalizes important geometric equations, like static vacuum and static perfect fluid. We investigate some geometric inequalities for those manifolds. Then, we established boundary estimates in terms of the first eigenvalue of the Jacobi operator and another one related to the Brown-York mass.