Vol. 13, No. 5, 2020

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Unconditional existence of conformally hyperbolic Yamabe flows

Mario B. Schulz

Vol. 13 (2020), No. 5, 1579–1590
Abstract

We prove global existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension m 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