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arXiv · 2304.05373

Einstein-Yang-Mills fields in conformally compact manifolds

Levi Lopes de Lima
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Abstract

We study the deformation theory of Einstein-Yang-Mills fields over conformally compact, asymptotically locally hyperbolic manifolds. We prove that if an Einstein-Yang-Mills field $(g_0,\omega_0)$ is trivial (which means that $g_0$ is Poincar\'e-Einstein and $\omega_0$ is a flat connection on a principal bundle over the underlying manifold) and non-degenerate in the appropriate sense then any sufficiently small perturbation of its boundary data at infinity may be realized as the boundary data of some Einstein-Yang-Mills field. This result is obtained as an application of the $0$-calculus of Mazzeo and Melrose and may be viewed as a natural extension of previous results by Graham-Lee, Lee and Usula.

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Levi Lopes de Lima. 2023-04-11. Einstein-Yang-Mills fields in conformally compact manifolds. https://arxiv.org/abs/2304.05373

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