Details
| Original language | English |
|---|---|
| Pages (from-to) | 477-510 |
| Number of pages | 34 |
| Journal | Analysis and PDE |
| Volume | 16 |
| Issue number | 2 |
| Publication status | Published - 3 May 2023 |
Abstract
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.
Keywords
- geometric evolution equations, nonlinear parabolic equations, positive scalar curvature, singular spaces, Yamabe flow
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Applied Mathematics
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In: Analysis and PDE, Vol. 16, No. 2, 03.05.2023, p. 477-510.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Long Time Existence of Yamabe Flow on Singular Spaces with Positive Yamabe Constant
AU - Lye, Jørgen Olsen
AU - Vertman, Boris
PY - 2023/5/3
Y1 - 2023/5/3
N2 - 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.
AB - 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.
KW - geometric evolution equations
KW - nonlinear parabolic equations
KW - positive scalar curvature
KW - singular spaces
KW - Yamabe flow
UR - http://www.scopus.com/inward/record.url?scp=85159202856&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2006.01544
DO - 10.48550/arXiv.2006.01544
M3 - Article
AN - SCOPUS:85159202856
VL - 16
SP - 477
EP - 510
JO - Analysis and PDE
JF - Analysis and PDE
SN - 2157-5045
IS - 2
ER -