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.

Unconditional existence of conformally hyperbolic Yamabe flows / Schulz, Mario B.. - In: ANALYSIS & PDE. - ISSN 1948-206X. - 13:5(2020), pp. 1579-1590. [10.2140/apde.2020.13.1579]

Unconditional existence of conformally hyperbolic Yamabe flows

Schulz, Mario B.
2020-01-01

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.
2020
5
Schulz, Mario B.
Unconditional existence of conformally hyperbolic Yamabe flows / Schulz, Mario B.. - In: ANALYSIS & PDE. - ISSN 1948-206X. - 13:5(2020), pp. 1579-1590. [10.2140/apde.2020.13.1579]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/439560
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