# Geometrically finite Poincar\'e-Einstein metrics

## TL;DR

This paper introduces new Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics, utilizing the inverse function theorem in weighted H"older spaces to construct these examples.

## Contribution

It presents a novel method for constructing Einstein metrics through perturbation techniques and functional analysis in weighted H"older spaces.

## Key findings

- New Einstein metrics constructed from hyperbolic metrics.
- Application of inverse function theorem in geometric analysis.
- Extension of Einstein metric examples to geometrically finite cases.

## Abstract

We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.