Year: 2025
Type: preprint
Abstract: In this paper, we prove a rigidity theorem for Poincaré-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 Poincaré-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.
Source: arXiv (Cornell University)
Authors: Lee, Sanghoon, Wang, Fang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910751537
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