Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 561-615 |
| Seitenumfang | 55 |
| Fachzeitschrift | Tohoku Mathematical Journal |
| Jahrgang | 75 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - 2023 |
| Extern publiziert | Ja |
Abstract
In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low-energy condition. We also prove a concentration-compactness dichotomy, and investigate what the alternatives to convergence are. We end by investigating a non-convergent example due to Viaclovsky in more detail.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Tohoku Mathematical Journal, Jahrgang 75, Nr. 4, 2023, S. 561-615.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Convergence of the Yamabe flow on singular spaces with positive Yamabe constant
AU - Carron, Gilles
AU - Lye, Jørgen Olsen
AU - Vertman, Boris
N1 - Funding Information: 2020 Mathematics Subject Classification. Primary 53C18; Secondary 58J35, 35K59. Key words and phrases. Yamabe flow, singular analysis, positive scalar curvature. The first author is partially supported by the ANR grant ANR-17-CE40-0034: CCEM and ANR-18-CE40-0012: RAGE and he thanks the Centre Henri Lebesgue ANR-11-LABX-0020-01 for creating an attractive mathematical environment.
PY - 2023
Y1 - 2023
N2 - In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low-energy condition. We also prove a concentration-compactness dichotomy, and investigate what the alternatives to convergence are. We end by investigating a non-convergent example due to Viaclovsky in more detail.
AB - In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low-energy condition. We also prove a concentration-compactness dichotomy, and investigate what the alternatives to convergence are. We end by investigating a non-convergent example due to Viaclovsky in more detail.
KW - positive scalar curvature
KW - singular analysis
KW - Yamabe flow
UR - http://www.scopus.com/inward/record.url?scp=85180520574&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2106.01799
DO - 10.48550/arXiv.2106.01799
M3 - Article
AN - SCOPUS:85180520574
VL - 75
SP - 561
EP - 615
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
SN - 0040-8735
IS - 4
ER -