arXiv Open Access 2021

A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy

Pak-Yeung Chan Zilu Ma Yongjia Zhang

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Abstrak

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 $ν$-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.

Topik & Kata Kunci

math.DG

Penulis (3)

Pak-Yeung Chan

Zilu Ma

Yongjia Zhang

Format Sitasi

APA MLA BibTeX

Chan, P., Ma, Z., Zhang, Y. (2021). A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy. https://arxiv.org/abs/2107.01419

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓