Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity

Details Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity

2011-09-26

arxiv.org/abs/1109.5456v2

Mathematics

Differential Geometry

25 pages

Scientific paper

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum $(M^n,g,V),$ we also compute the asymptotic expansions of $g$ and $V$ at conformal infinity.

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