A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy
Differential Geometry
2021-07-06 v1
Abstract
This note is a continuation of [CMZ21]. We shall show that an ancient Ricci flow with uniformly bounded Nash entropy must also have uniformly bounded -functional. Consequently, on such an ancient solution there are uniform logarithmic Sobolev and Sobolev inequalities. We emphasize that the main theorem in this paper is true so long as the theory in [Bam20c] is valid, and in particular, when the underlying manifold is closed.
Keywords
Cite
@article{arxiv.2107.01419,
title = {A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy},
author = {Pak-Yeung Chan and Zilu Ma and Yongjia Zhang},
journal= {arXiv preprint arXiv:2107.01419},
year = {2021}
}