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#### Minimal data at a given point of space for solutions to certain geometric systems

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1001.2230

(Preprint), 281KB

CQG_27_15_155006.pdf

(Any fulltext), 264KB

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##### Citation

Acena, A. E. (2010). Minimal data at a given point of space for solutions to certain
geometric systems.* Classical and quantum gravity,* *27*(15):
155006. doi:10.1088/0264-9381/27/15/155006.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-69AD-1

##### Abstract

We consider a geometrical system of equations for a three dimensional
Riemannian manifold. This system of equations has been constructed as to
include several physically interesting systems of equations, such as the
stationary Einstein vacuum field equations or harmonic maps coupled to gravity
in three dimensions. We give a characterization of its solutions in a
neighbourhood of a given point through sequences of symmetric trace free
tensors (referred to as `null data'). We show that the null data determine a
formal expansion of the solution and we obtain necessary and sufficient growth
estimates on the null data for the formal expansion to be absolutely convergent
in a neighbourhood of the given point. This provides a complete
characterization of all the solutions to the given system of equations around
that point.