Compacitification and positive mass theorem for fibered Euclidean end

TL;DR

This paper investigates the positive mass theorem for certain fibered Euclidean end manifolds by exploring their compactification, extending the understanding of mass in geometric analysis.

Contribution

It introduces a new approach to the positive mass theorem for manifolds asymptotic to a product space with fibered Euclidean ends through compactification techniques.

Findings

Established conditions under which the positive mass theorem holds for fibered Euclidean ends.

Connected the compactification problem with mass positivity in geometric analysis.

Extended classical results to manifolds with fibered asymptotic geometry.

Abstract

In this note, we consider the positive mass theorem for Riemannian manifolds $(M^{n},g)$ asymptotic to $(\mathbb{R}^{k}\times X^{n-k}, g_{\mathbb{R}^{k}}+g_{X})$ for $k\geq 3$ by studying the corresponding compactification problem.