New Proofs of Perelman’s Theorem on Shrinking Breathers in Ricci Flow

Peng Lu; Yu Zheng

doi:10.1007/s12220-017-9974-1

New Proofs of Perelman’s Theorem on Shrinking Breathers in Ricci Flow

Peng Lu
, Yu Zheng^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Oregon

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

4 Scopus citations

Abstract

We give two new proofs of Perelman’s theorem that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons, using the fact that the singularity models of Type I solutions are shrinking gradient Ricci solitons and the fact that non-collapsed Type I ancient solutions have rescaled limits being shrinking gradient Ricci solitons.

Original language	English
Pages (from-to)	3718-3724
Number of pages	7
Journal	Journal of Geometric Analysis
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s12220-017-9974-1
State	Published - 15 Dec 2018

Keywords

Gradient Ricci solitons
Ricci flow
Shrinking breathers
Type I solutions

Access to Document

10.1007/s12220-017-9974-1

Cite this

@article{27b1878f489c4cfcb54f7d4c18683d6c,

title = "New Proofs of Perelman{\textquoteright}s Theorem on Shrinking Breathers in Ricci Flow",

abstract = "We give two new proofs of Perelman{\textquoteright}s theorem that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons, using the fact that the singularity models of Type I solutions are shrinking gradient Ricci solitons and the fact that non-collapsed Type I ancient solutions have rescaled limits being shrinking gradient Ricci solitons.",

keywords = "Gradient Ricci solitons, Ricci flow, Shrinking breathers, Type I solutions",

author = "Peng Lu and Yu Zheng",

note = "Publisher Copyright: {\textcopyright} 2017, Mathematica Josephina, Inc.",

year = "2018",

month = dec,

day = "15",

doi = "10.1007/s12220-017-9974-1",

language = "英语",

volume = "28",

pages = "3718--3724",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - New Proofs of Perelman’s Theorem on Shrinking Breathers in Ricci Flow

AU - Lu, Peng

AU - Zheng, Yu

PY - 2018/12/15

Y1 - 2018/12/15

N2 - We give two new proofs of Perelman’s theorem that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons, using the fact that the singularity models of Type I solutions are shrinking gradient Ricci solitons and the fact that non-collapsed Type I ancient solutions have rescaled limits being shrinking gradient Ricci solitons.

AB - We give two new proofs of Perelman’s theorem that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons, using the fact that the singularity models of Type I solutions are shrinking gradient Ricci solitons and the fact that non-collapsed Type I ancient solutions have rescaled limits being shrinking gradient Ricci solitons.

KW - Gradient Ricci solitons

KW - Ricci flow

KW - Shrinking breathers

KW - Type I solutions

UR - https://www.scopus.com/pages/publications/85037625757

U2 - 10.1007/s12220-017-9974-1

DO - 10.1007/s12220-017-9974-1

M3 - 文章

AN - SCOPUS:85037625757

SN - 1050-6926

VL - 28

SP - 3718

EP - 3724

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 4

ER -

New Proofs of Perelman’s Theorem on Shrinking Breathers in Ricci Flow

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this