Unconditional existence of conformally hyperbolic Yamabe flows

Abstract

We prove global existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension $m\ge 3$ 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.

References in corpus (6)

• Existence of Ricci flows of incomplete surfaces
• Uniqueness of Instantaneously Complete Ricci flows
• Radial Fast Diffusion on the Hyperbolic Space
• Instantaneously complete Yamabe flow on hyperbolic space
• Yamabe flow on non-compact manifolds with unbounded initial curvature
• Ricci flows with unbounded curvature

Cited by in corpus (3)

• Incomplete Yamabe flows and removable singularities
• The Yamabe flow on asymptotically flat manifolds
• Infinite-time incompleteness of noncompact Yamabe flow