Embeddings, immersions and the Bartnik quasi-local mass conjectures
| Autor: | Anderson, Michael T., Jauregui, Jeffrey L. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Ann. Henri Poincar\'e, Vol. 20, No. 5 (2019), pg. 1651--1698 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00023-019-00786-3 |
| Popis: | Given a Riemannian 3-ball $(\bar B, g)$ of non-negative scalar curvature, Bartnik conjectured that $(\bar B, g)$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined by natural geometric conditions on the boundary data of $(\bar B, g)$. We prove the validity of the second statement, i.e.~such mass-minimizers, if they exist, are indeed AF solutions of the static vacuum equations. On the other hand, we prove that the first statement is not true in general; there is a rather large class of bodies $(\bar B, g)$ for which a minimal mass extension does not exist. Comment: 38 pages, 4 figures |
| Databáze: | arXiv |
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