Green function rigidity and the mass of hypersurfaces under inversion

Xuezhang Chen; Jiaxue Gan; Yalong Shi

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arXiv · 2501.15805

Green function rigidity and the mass of hypersurfaces under inversion

Xuezhang Chen·Jiaxue Gan·Yalong Shi

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Abstract

This is a sequel to arXiv:2401.02087. We prove the Green function rigidity conjecture in arXiv:2401.02087 for conformal Laplacian in dimension $n\geq 3$. For the Paneitz operator, we prove the Green function rigidity conjecture when $n\neq 4k+2, k\geq 2$. Important ingredients in our proof are the positive mass theorem and the positive energy theorem for Paneitz operator. As a byproduct, we also obtain a new formula for the ADM mass of an asymptotically flat hypersurface that allows for a non-entire graph.

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BibTeX RIS

Xuezhang Chen, Jiaxue Gan, Yalong Shi. 2025-01-27. Green function rigidity and the mass of hypersurfaces under inversion. https://arxiv.org/abs/2501.15805

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