Unconditional existence of conformally hyperbolic Yamabe flows
Copyright policy )Unconditional existence of conformally hyperbolic Yamabe flows
We prove global existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension $m\geq3$ starting from any smooth, conformally hyperbolic initial metric. We do not require initial completeness or curvature bounds. With the same methods, we show rigidity of hyperbolic space under the Yamabe flow.
- Université de Cergy Pontoise France
- UNIVERSITE DE CERGY-PONTOISE France
- Université de Cergy-Pontoise France
- University of California System United States
- UNIVERSITE DE CERGY-PONTOISE France
Mathematics - Differential Geometry, 35A01, Instantaneously complete; Unbounded curvature; Yamabe flow, fast diffusion equation, 35K65, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, instantaneously complete, 53C44, 35A02, hyperbolic space, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Ricci flows, 35K55, Yamabe flow, FOS: Mathematics, Nonlinear parabolic equations, unbounded curvature, Geometric evolution equations, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, 35A01, Instantaneously complete; Unbounded curvature; Yamabe flow, fast diffusion equation, 35K65, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, instantaneously complete, 53C44, 35A02, hyperbolic space, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Ricci flows, 35K55, Yamabe flow, FOS: Mathematics, Nonlinear parabolic equations, unbounded curvature, Geometric evolution equations, Analysis of PDEs (math.AP)
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