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arXiv · 2503.06062

Rigidity of Poincar\'e-Einstein manifolds with flat Euclidean conformal infinity

Sanghoon Lee·Fang Wang
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Abstract

In this paper, we prove a rigidity theorem for Poincar\'e-Einstein manifolds whose conformal infinity is a flat Euclidean space. The proof relies on analyzing the propagation of curvature tensors over the level sets of an adapted boundary defining function. Additionally, we provide examples of Poincar\'e-Einstein manifolds with non-compact conformal infinities. Furthermore, we draw analogies with Ricci-flat manifolds exhibiting Euclidean volume growth, particularly when the compactified metric has non-negative scalar curvature.

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Sanghoon Lee, Fang Wang. 2025-03-08. Rigidity of Poincar\'e-Einstein manifolds with flat Euclidean conformal infinity. https://arxiv.org/abs/2503.06062

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