Perturbative solutions to the extended constant scalar curvature equations on asymptotically hyperbolic manifolds

TL;DR

This paper establishes local existence results for solutions to extended constant scalar curvature equations on asymptotically hyperbolic manifolds, enabling new constructions of such metrics with constant scalar curvature.

Contribution

It provides the first local existence proof for these equations in the asymptotically hyperbolic setting, expanding the toolkit for geometric analysis.

Findings

Proved local existence of solutions to the extended constant scalar curvature equations.

Constructed new asymptotically hyperbolic metrics with constant scalar curvature.

Extended the applicability of these equations to geometric problems.

Abstract

We prove local existence of solutions to the extended constant scalar curvature equations introduced by A. Butscher, in the asymptotically hyperbolic setting. This gives a new local construction of asymptotically hyperbolic metrics with constant scalar curvature.