Unconditional existence of conformally hyperbolic Yamabe flows

Schulz, Mario B.

doi:10.2140/apde.2020.13.1579

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Unconditional existence of conformally hyperbolic Yamabe flows

Mario B. Schulz

Vol. 13 (2020), No. 5, 1579–1590

DOI: 10.2140/apde.2020.13.1579

Abstract

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

Keywords

Yamabe flow, instantaneously complete, unbounded curvature

Mathematical Subject Classification 2010

Primary: 35A01, 35K55, 53C44

Secondary: 35A02, 35K65

Milestones

Received: 17 December 2018

Accepted: 31 May 2019

Published: 27 July 2020

Authors

Mario B. Schulz
ETH Zürich Zürich Switzerland

Vol. 13, No. 5, 2020