#### 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 $m\ge 3$ 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.

##### Keywords
Yamabe flow, instantaneously complete, unbounded curvature
##### Mathematical Subject Classification 2010
Primary: 35A01, 35K55, 53C44
Secondary: 35A02, 35K65