Metric gradient flows and variational principles

Alberto Domínguez Corella

Metric gradient flows and variational principles

Functional Analysis 2026-08-02 v1 Analysis of PDEs

Authors: Alberto Domínguez Corella

Abstract

We show that Ekeland-type variational principles can be derived from steepest descent curves in metric spaces. From this, we relate the existence of the Calabi flow to the validity of the Ekeland variational principle for the $K$ -energy on the space of K\"ahler potentials.

Cite

@article{arxiv.2608.01262,
  title  = {Metric gradient flows and variational principles},
  author = {Alberto Domínguez Corella},
  journal= {arXiv preprint arXiv:2608.01262},
  year   = {2026}
}