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Metric gradient flows and variational principles
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 Kähler potentials.
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BibTeX
@misc{corella2026metric,
title = {{Metric gradient flows and variational principles}},
author = {Alberto Domínguez Corella},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.01262},
eprint = {2608.01262},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.01262},
}
RIS
TY - UNPB
TI - Metric gradient flows and variational principles
AU - Alberto Domínguez Corella
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2608.01262
UR - https://arxiv.org/abs/2608.01262
AB - 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 Kähler potentials.
ER -