Tohoku Mathematical Journal
2023
December
SECOND SERIES VOL. 75, NO. 4

Tohoku Math. J.
75 (2023), 561-615

Title CONVERGENCE OF THE YAMABE FLOW ON SINGULAR SPACES WITH POSITIVE YAMABE CONSTANT

Author Gilles Carron, Jørgen Olsen Lye and Boris Vertman

(Received January 5, 2022, revised June 15, 2022)
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.

Mathematics Subject Classification. Primary 53C18; Secondary 58J35, 35K59.
Key words and phrases. Yamabe flow, singular analysis, positive scalar curvature.

To the top of this page

Back to the Contents