Short-time existence of solutions to the cross curvature flow on 3-manifolds

被引：18

作者：

Buckland, JA ^{[1
]}

机构：

[1] Australian Natl Univ, Inst Math Sci, Ctr Math & Appl, Canberra, ACT 0200, Australia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 06期

关键词：

nonlinear evolution equations; curvature flow; short-time existence;

D O I：

10.1090/S0002-9939-05-08204-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a compact 3-manifold with an initial Riemannian metric of positive (or negative) sectional curvature, we prove the short-time existence of a solution to the cross curvature flow. This is achieved using an idea first introduced by DeTurck (1983) in his work establishing the short-time existence of solutions to the Ricci flow.

引用

页码：1803 / 1807

页数：5

共 50 条

[1] Examples for cross curvature flow on 3-manifolds
Li Ma
Dezhong Chen
Calculus of Variations and Partial Differential Equations, 2006, 26 : 227 - 243
[2] Examples for cross curvature flow on 3-manifolds
Ma, L
Chen, DZ
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 26 (02) : 227 - 243
[3] SHORT-TIME EXISTENCE OF THE RICCI FLOW ON NONCOMPACT RIEMANNIAN MANIFOLDS
Xu, Guoyi
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (11) : 5605 - 5654
[4] The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature
Liao, Wei-Hung
TURKISH JOURNAL OF MATHEMATICS, 2019, 43 (05) : 2444 - 2450
[5] Short-time Existence of Inverse Mean Curvature Flow with External Force Field
Liu, Yannan
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON INFORMATION AND MANAGEMENT SCIENCES, 2010, 9 : 516 - 517
[6] Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature
Bennett Chow
David Glickenstein
Peng Lu
Mathematische Zeitschrift, 2006, 254 : 1 - 28
[7] Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature
Chow, Bennett
Glickenstein, David
Lu, Peng
MATHEMATISCHE ZEITSCHRIFT, 2006, 254 (01) : 1 - 28
[8] Short-time existence for the network flow
Lira, Jorge
Mazzeo, Rafe
Pluda, Alessandra
Saez, Mariel
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2023, 76 (12) : 3968 - 4021
[9] Scalar curvature and the existence of geometric structures on 3-manifolds, II
Anderson, MT
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2003, 563 : 115 - 195
[10] Scalar curvature and the existence of geometric structures on 3-manifolds, I
Anderson, MT
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2002, 553 : 125 - 182

← 1 2 3 4 5 →