Mass, Kähler manifolds, and symplectic geometry
| Autor: | Claude LeBrun |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
010102 general mathematics Dimension (graph theory) Kähler manifold Complex dimension 01 natural sciences Mass formula Differential geometry 0103 physical sciences Euclidean geometry Metric (mathematics) 010307 mathematical physics Geometry and Topology 0101 mathematics Analysis Symplectic geometry Mathematics |
| Zdroj: | Annals of Global Analysis and Geometry. 56:97-112 |
| ISSN: | 1572-9060 0232-704X |
| Popis: | In the author’s previous joint work with Hein (Commun Math Phys 347:183–221, 2016), a mass formula for asymptotically locally Euclidean Kahler manifolds was proved, assuming only relatively weak fall-off conditions on the metric. However, the case of real dimension 4 presented technical difficulties that led us to require fall-off conditions in this special dimension that are stronger than the Chruściel fall-off conditions that sufficed in higher dimensions. Nevertheless, the present article shows that techniques of four-dimensional symplectic geometry can be used to obtain all the major results of Hein-LeBrun (2016), assuming only Chruściel-type fall-off. In particular, the present article presents a new proof of our Penrose-type inequality for the mass of an asymptotically Euclidean Kahler manifold that only requires this very weak metric fall-off. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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