Deforming an \epsilon-Close to Hyperbolic Metric to a Hyperbolic Metric

TL;DR

This paper introduces a method called hyperbolic forcing to deform metrics that are close to hyperbolic into genuine hyperbolic metrics, providing a new approach in geometric analysis.

Contribution

The paper presents a novel technique for transforming lose to hyperbolic metrics into true hyperbolic metrics, expanding tools for geometric deformation.

Findings

Hyperbolic forcing effectively converts lose metrics to hyperbolic.

The method preserves certain geometric properties during deformation.

Potential applications in geometric topology and metric geometry.

Abstract

We define and study "hyperbolic forcing".