Conformal deformations of CAT(0) spaces

TL;DR

This paper demonstrates that CAT(0) spaces remain CAT(0) under certain conformal deformations, allowing for a wide range of non-trivial geometric modifications while preserving their fundamental properties.

Contribution

It establishes that the class of CAT(0) spaces is closed under specific conformal deformations, expanding the understanding of their geometric flexibility.

Findings

CAT(0) spaces are closed under certain conformal changes

Existence of diverse non-trivial deformations for CAT(0) spaces

Preservation of CAT(0) properties under these deformations

Abstract

We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.