Positive mass theorem for some asymptotically hyperbolic manifolds

TL;DR

This paper proves a positive mass theorem for certain asymptotically hyperbolic spin manifolds and explores implications for the Yamabe inequality, enhancing understanding of geometric invariants under surgeries.

Contribution

It introduces a positive mass theorem for specific asymptotically hyperbolic manifolds and connects it to the Yamabe inequality in noncompact settings.

Findings

Established a positive mass theorem for asymptotically hyperbolic spin manifolds.

Demonstrated the Yamabe inequality for certain noncompact manifolds.

Provided insights into the behavior of Yamabe invariants under surgeries.

Abstract

We prove a positive mass theorem for some noncompact spin manifolds that are asymptotic to products of hyperbolic space with a compact manifold. As conclusion we show the Yamabe inequality for some noncompact manifolds which are important to understand the behaviour of Yamabe invariants under surgeries.