Energy identity and necklessness for a sequence of Sacks Uhlenbeck maps to a sphere | |
Li, Jiayu1,2; Zhu, Xiangrong3 | |
2019 | |
Source Publication | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE |
ISSN | 0294-1449 |
Volume | 36Issue:1Pages:103-118 |
Abstract | Let u be a map from a Riemann surface M to a Riemannian manifold N and alpha > 1, the alpha energy functional is defined as E-alpha(u)= 1/2 integral[(l+vertical bar del u vertical bar(2))(alpha)-1]dV. We call u(alpha) a sequence of Sacks-Uhlenbeck maps if u(alpha) are critical points of E-alpha and sup(alpha>1)E(alpha)(u(alpha)) < infinity In this paper, we show the energy identity and necklessness for a sequence of Sacks Uhlenbeck maps during blowing up, if the target N is a sphere SK-1. The energy identity can be used to give an alternative proof of Perelman's result [15] that the Ricci flow from a compact orientable prime non-aspherical 3-dimensional manifold becomes extinct in finite time (cf. [3,4]). (C) 2018 Elsevier Masson SAS. All rights reserved. |
Keyword | Energy identity Sacks-Uhlenbeck map Harmonic sphere |
DOI | 10.1016/j.anihpc.2018.04.002 |
Language | 英语 |
Funding Project | NSFC[11131007] ; NSFC[11071236] ; NSFC[11471288] ; NSFC[11721101] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000456754200005 |
Publisher | ELSEVIER SCIENCE BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/32353 |
Collection | 数学所 |
Affiliation | 1.Univ Sci & Technol China, Coll Math Sci, Hefei 230026, Anhui, Peoples R China 2.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China 3.Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China |
Recommended Citation GB/T 7714 | Li, Jiayu,Zhu, Xiangrong. Energy identity and necklessness for a sequence of Sacks Uhlenbeck maps to a sphere[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE,2019,36(1):103-118. |
APA | Li, Jiayu,&Zhu, Xiangrong.(2019).Energy identity and necklessness for a sequence of Sacks Uhlenbeck maps to a sphere.ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE,36(1),103-118. |
MLA | Li, Jiayu,et al."Energy identity and necklessness for a sequence of Sacks Uhlenbeck maps to a sphere".ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE 36.1(2019):103-118. |
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