Four-dimensional generalized Ricci flows with nilpotent symmetry

被引：0

作者：

Gindi, Steven ^{[1
]}

Streets, Jeffrey ^{[2
]}

机构：

[1] Binghamton Univ, Whitney Hall, Binghamton, NY 13902 USA

[2] Univ Calif Irvine, Rowland Hall, Irvine, CA 92617 USA

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2023年 / 25卷 / 07期

关键词：

Generalized Ricci flow; T-DUALITY; RENORMALIZATION; REGULARITY; GEOMETRY; ENTROPY;

D O I：

10.1142/S0219199722500250

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension 1 symmetry. We show that. all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.

引用

页数：28

共 20 条

[1] STRINGS IN BACKGROUND FIELDS
CALLAN, CG
FRIEDAN, D
MARTINEC, EJ
PERRY, MJ
[J]. NUCLEAR PHYSICS B, 1985, 262 (04) : 593 - 609
[2] Cheeger J., 1992, J. Amer. Math. Soc., V5, P327
[3] Entropy and reduced distance for Ricci expanders
Feldman, M
Ilmanen, T
Ni, L
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2005, 15 (01) : 49 - 62
[4] Garcia-Fernandez M., 2021, AMSUNIVERSITY LECT S
[5] Ricci flow, Killing spinors, and T-duality in generalized geometry
Garcia-Fernandez, Mario
[J]. ADVANCES IN MATHEMATICS, 2019, 350 : 1059 - 1108
[6] Structure of Collapsing Solutions of Generalized Ricci Flow
Gindi, Steven
Streets, Jeffrey
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (04) : 4253 - 4286
[7] A COMPACTNESS PROPERTY FOR SOLUTIONS OF THE RICCI FLOW
HAMILTON, RS
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1995, 117 (03) : 545 - 572
[8] Huang S., 2020, ARXIV
[9] ISENBERG J, 1992, J DIFFER GEOM, V35, P723
[10] On the long-time behavior of type-III Ricci flow solutions
Lott, John
[J]. MATHEMATISCHE ANNALEN, 2007, 339 (03) : 627 - 666

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