LONG TIME EXISTENCE OF YAMABE FLOW ON SINGULAR SPACES WITH POSITIVE YAMABE CONSTANT

被引：2

作者：

Lye, Jorgen Olsen ^{[1
]}

Vertman, Boris ^{[2
]}

机构：

[1] Leibniz Univ Hannover, Inst Differentialgeometrie, Hannover, Germany

[2] Carl von Ossietzky Univ Oldenburg, Inst Math, Oldenburg, Germany

来源：

ANALYSIS & PDE | 2023年 / 16卷 / 02期

关键词：

geometric evolution equations; Yamabe flow; positive scalar curvature; singular spaces; nonlinear parabolic equations; CONVERGENCE; MANIFOLDS; METRICS;

D O I：

10.2140/apde.2023.16.477

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish long-time existence of the normalized Yamabe flow with positive Yamabe constant on a class of manifolds that includes spaces with incomplete cone-edge singularities. We formulate our results axiomatically so that they extend to general stratified spaces as well, provided certain parabolic Schauder estimates hold. The central analytic tool is a parabolic Moser iteration, which yields uniform upper and lower bounds on both the solution and the scalar curvature.

引用

页码：477 / 510

页数：35

共 20 条

[11] Yamabe flow and metrics of constant scalar curvature on a complete manifold
Ma, Li
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (01)
[12] Infinite-time incompleteness of noncompact Yamabe flow
Takahashi, Jin
Yamamoto, Hikaru
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022, 61 (06)
[13] Yamabe flow and locally conformally flat manifolds with positive pinched Ricci curvature
Cheng, Liang
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2025, 64 (03)
[14] Infinite-time blowing-up solutions to small perturbations of the Yamabe flow
Kim, Seunghyeok
Musso, Monica
ADVANCES IN MATHEMATICS, 2024, 443
[15] The Long-Time Existence of the Finslerian Ricci Flow
Ahmadi, Mohamad Yar
Bidabad, Behroz
Shahi, Alireza
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2024, 50 (02)
[16] Long time existence of Ricci-harmonic flow
Li, Yi
FRONTIERS OF MATHEMATICS IN CHINA, 2016, 11 (05) : 1313 - 1334
[17] Long time existence of solutions to an elastic flow of networks
Garcke, Harald
Menzel, Julia
Pluda, Alessandra
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2020, 45 (10) : 1253 - 1305
[18] On long-time existence for the flow of static metrics with rotational symmetry
Gulcev, Liljana
Oliynyk, Todd A.
Woolgar, Eric
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2010, 18 (04) : 705 - 741
[19] Long time existence and bounded scalar curvature in the Ricci-harmonic flow
Li, Yi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (01) : 69 - 97
[20] GLOBAL EXISTENCE AND LONG-TIME BEHAVIOR OF ENTROPY WEAK SOLUTIONS TO A QUASILINEAR HYPERBOLIC BLOOD FLOW MODEL
Li, Tong
Zhao, Kun
NETWORKS AND HETEROGENEOUS MEDIA, 2011, 6 (04) : 625 - 646

← 1 2 →