Convergence of the Yamabe flow on singular spaces with positive Yamabe constant
Copyright policy )Convergence of the Yamabe flow on singular spaces with positive Yamabe constant
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
- University of Nantes France
- Université de Nantes France
metric measure spaces, positive scalar curvature, Analysis of PDEs, Heat and other parabolic equation methods for PDEs on manifolds, Conformal structures on manifolds, 510, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Yamabe flow, FOS: Mathematics, Geometric evolution equations, Differential Geometry, Analysis of PDEs (math.AP), 53C44, 58J35, 35K08
metric measure spaces, positive scalar curvature, Analysis of PDEs, Heat and other parabolic equation methods for PDEs on manifolds, Conformal structures on manifolds, 510, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Yamabe flow, FOS: Mathematics, Geometric evolution equations, Differential Geometry, Analysis of PDEs (math.AP), 53C44, 58J35, 35K08
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