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arXiv · 1911.06754

Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds

Hubert L. Bray·Demetre P. Kazaras·Marcus A. Khuri·Daniel L. Stern
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Abstract

An explicit lower bound for the mass of an asymptotically flat Riemannian 3-manifold is given in terms of linear growth harmonic functions and scalar curvature. As a consequence, a new proof of the positive mass theorem is achieved in dimension three. The proof has parallels with both the Schoen-Yau minimal hypersurface technique and Witten's spinorial approach. In particular, the role of harmonic spinors and the Lichnerowicz formula in Witten's argument is replaced by that of harmonic functions and a formula introduced by the fourth named author in recent work, while the level sets of harmonic functions take on a role similar to that of the Schoen-Yau minimal hypersurfaces.

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Hubert L. Bray, Demetre P. Kazaras, Marcus A. Khuri, Daniel L. Stern. 2019-11-15. Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds. https://arxiv.org/abs/1911.06754

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