Mass and polyhedra in asymptotically hyperbolic manifolds

TL;DR

This paper evaluates a component of the hyperbolic mass functional on specific polyhedra within the upper half space model, extending previous formulas by Miao-Piubello to better understand asymptotically hyperbolic manifolds.

Contribution

It introduces a new evaluation of the hyperbolic mass functional on polyhedra, extending existing formulas to the context of asymptotically hyperbolic manifolds.

Findings

Explicit evaluation of hyperbolic mass component on polyhedra

Extension of Miao-Piubello formula to new geometric settings

Insights into geometric properties of asymptotically hyperbolic spaces

Abstract

Using the upper half space model, we evaluate a component of the hyperbolic mass functional evaluated on a special family of polyhedra extending a formula of Miao-Piubello.