Long time existence of Yamabe flow on singular spaces with positive Yamabe constant
Copyright policy )Long time existence of Yamabe flow on singular spaces with positive Yamabe constant
In this work 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 our results 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.
36 pages,
Mathematics - Differential Geometry, positive scalar curvature, Flows related to mean curvature, nonlinear parabolic equations, Heat and other parabolic equation methods for PDEs on manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Yamabe flow, FOS: Mathematics, geometric evolution equations, singular spaces, Heat kernel, Analysis of PDEs (math.AP), 53C44, 58J35, 35K08
Mathematics - Differential Geometry, positive scalar curvature, Flows related to mean curvature, nonlinear parabolic equations, Heat and other parabolic equation methods for PDEs on manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Yamabe flow, FOS: Mathematics, geometric evolution equations, singular spaces, Heat kernel, Analysis of PDEs (math.AP), 53C44, 58J35, 35K08
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