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.File in questo prodotto:
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