Time-dependent gradient curves on CAT(0) spaces

TL;DR

This paper introduces a novel approach to studying time-dependent gradient curves specifically within CAT(0) spaces, providing insights distinct from more general flow frameworks.

Contribution

It develops a specialized method for gradient curves in CAT(0) spaces, differing from prior work that considers broader flow settings without focusing on CAT(0) geometry.

Findings

Applicable to flows not covered by previous methods

Provides a new perspective on gradient curves in CAT(0) spaces

Distinguishes from Kim-Masmoudi's more general flow framework

Abstract

This is a preliminary version dated Dec. 2013. It was written independently of [Kim-Masmoudi reference] which uses a similar method. [KM] works with flows in a more general setting and does not mention CAT(K) geometry and gradient curves. There are flows to which our method applies that do not satisfy the conditions in [KM].