Math @ Duke

Publications [#354059] of Demetre P Kazaras
Papers Submitted
 Hubert L. Bray, Demetre P. Kazaras, Marcus A. Khuri, Daniel L. Stern, Harmonic Functions and The Mass of 3Dimensional Asymptotically Flat Riemannian Manifolds
(2020)
(last updated on 2020/12/18)
Abstract: An explicit lower bound for the mass of an asymptotically flat Riemannian 3manifold 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 SchoenYau 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 SchoenYau minimal hypersurfaces.


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