Kählerity of Shrinking Gradient Ricci Solitons Asymptotic to Kähler Cones

Research output: Contribution to journalArticle

Abstract

We prove that a shrinking gradient Ricci soliton which is asymptotic to a Kähler cone along some end is itself Kähler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally Kähler.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalJournal of Geometric Analysis
DOIs
StateAccepted/In press - Oct 4 2017

Fingerprint

Ricci Soliton
Shrinking
Cone
Infinity
Gradient

Keywords

  • Kählerity
  • Ricci flow
  • Ricci solitons

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Kählerity of Shrinking Gradient Ricci Solitons Asymptotic to Kähler Cones. / Kotschwar, Brett.

In: Journal of Geometric Analysis, 04.10.2017, p. 1-15.

Research output: Contribution to journalArticle

@article{053f4af1321447219606b6d90d606f77,
title = "K{\"a}hlerity of Shrinking Gradient Ricci Solitons Asymptotic to K{\"a}hler Cones",
abstract = "We prove that a shrinking gradient Ricci soliton which is asymptotic to a K{\"a}hler cone along some end is itself K{\"a}hler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally K{\"a}hler.",
keywords = "K{\"a}hlerity, Ricci flow, Ricci solitons",
author = "Brett Kotschwar",
year = "2017",
month = "10",
day = "4",
doi = "10.1007/s12220-017-9922-0",
language = "English (US)",
pages = "1--15",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",

}

TY - JOUR

T1 - Kählerity of Shrinking Gradient Ricci Solitons Asymptotic to Kähler Cones

AU - Kotschwar, Brett

PY - 2017/10/4

Y1 - 2017/10/4

N2 - We prove that a shrinking gradient Ricci soliton which is asymptotic to a Kähler cone along some end is itself Kähler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally Kähler.

AB - We prove that a shrinking gradient Ricci soliton which is asymptotic to a Kähler cone along some end is itself Kähler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally Kähler.

KW - Kählerity

KW - Ricci flow

KW - Ricci solitons

UR - http://www.scopus.com/inward/record.url?scp=85030682006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030682006&partnerID=8YFLogxK

U2 - 10.1007/s12220-017-9922-0

DO - 10.1007/s12220-017-9922-0

M3 - Article

AN - SCOPUS:85030682006

SP - 1

EP - 15

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

ER -