Uniqueness of Instantaneously Complete Ricci flows

Abstract

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [23, 11], this completes the well-posedness theory for instantaneously complete Ricci flows on surfaces.

References in corpus (5)

• Existence of Ricci flows of incomplete surfaces
• Ricci flow of negatively curved incomplete surfaces
• Ricci flow and the determinant of the Laplacian on non-compact surfaces
• Canonical smoothing of compact Alexandrov surfaces via Ricci flow
• Ricci flows with unbounded curvature

Cited by in corpus (10)

• Instantaneously complete Yamabe flow on hyperbolic space
• Ricci Solitons, Conical Singularities, and Nonuniqueness
• Yamabe flow on non-compact manifolds with unbounded initial curvature
• The Yamabe flow on incomplete manifolds
• Ricci flow from spaces with isolated conical singularities
• Loss of initial data under limits of Ricci flows
• Unconditional existence of conformally hyperbolic Yamabe flows
• Incomplete Yamabe flows and removable singularities
• Smoothing a measure on a Riemann surface using Ricci flow
• Infinite-time incompleteness of noncompact Yamabe flow