Uniform lipschitz continuity of the isoperimetric profile of compact surfaces under normalized ricci flow

Yizhong Zheng

doi:10.1090/proc/15367

Uniform lipschitz continuity of the isoperimetric profile of compact surfaces under normalized ricci flow

Yizhong Zheng^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

1 Citation (Scopus)

Abstract

We show that the isoperimetric profile h_g(t₎(ξ) of a compact Riemannian manifold (M, g) is jointly continuous when metrics g(t) vary continuously. We also show that, when M is a compact surface and g(t) evolves under normalized Ricci flow, h²_g(t₎(ξ) is uniform Lipschitz continuous and hence h_g(t₎(ξ) is uniform locally Lipschitz continuous.

Original language	English
Pages (from-to)	2105-2119
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	5
DOIs	https://doi.org/10.1090/proc/15367
Publication status	Published - May 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 American Mathematical Society

Keywords

Isoperimetric profile
Ricci flow

Access to Document

10.1090/proc/15367

Cite this

@article{0a36426438964d63a97abcc560fa84ce,

title = "Uniform lipschitz continuity of the isoperimetric profile of compact surfaces under normalized ricci flow",

abstract = "We show that the isoperimetric profile hg(t)(ξ) of a compact Riemannian manifold (M, g) is jointly continuous when metrics g(t) vary continuously. We also show that, when M is a compact surface and g(t) evolves under normalized Ricci flow, h2g(t)(ξ) is uniform Lipschitz continuous and hence hg(t)(ξ) is uniform locally Lipschitz continuous.",

keywords = "Isoperimetric profile, Ricci flow",

author = "Yizhong Zheng",

note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society",

year = "2021",

month = may,

doi = "10.1090/proc/15367",

language = "English",

volume = "149",

pages = "2105--2119",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "5",

}

TY - JOUR

T1 - Uniform lipschitz continuity of the isoperimetric profile of compact surfaces under normalized ricci flow

AU - Zheng, Yizhong

PY - 2021/5

Y1 - 2021/5

N2 - We show that the isoperimetric profile hg(t)(ξ) of a compact Riemannian manifold (M, g) is jointly continuous when metrics g(t) vary continuously. We also show that, when M is a compact surface and g(t) evolves under normalized Ricci flow, h2g(t)(ξ) is uniform Lipschitz continuous and hence hg(t)(ξ) is uniform locally Lipschitz continuous.

AB - We show that the isoperimetric profile hg(t)(ξ) of a compact Riemannian manifold (M, g) is jointly continuous when metrics g(t) vary continuously. We also show that, when M is a compact surface and g(t) evolves under normalized Ricci flow, h2g(t)(ξ) is uniform Lipschitz continuous and hence hg(t)(ξ) is uniform locally Lipschitz continuous.

KW - Isoperimetric profile

KW - Ricci flow

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000631285900025

UR - https://openalex.org/W3108295689

UR - https://www.scopus.com/pages/publications/85103009274

U2 - 10.1090/proc/15367

DO - 10.1090/proc/15367

M3 - Journal Article

SN - 0002-9939

VL - 149

SP - 2105

EP - 2119

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

Uniform lipschitz continuity of the isoperimetric profile of compact surfaces under normalized ricci flow

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this