Convergence of the Yamabe flow on singular spaces with positive Yamabe constant

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.

54 pages, 1 figure

References in corpus (2)

• Yamabe flow on non-compact manifolds with unbounded initial curvature
• Long-time existence of Yamabe flow on singular spaces with positive Yamabe constant

Cited by in corpus (1)

• Generalized Yamabe Flows