Existence and regularity of min-max anisotropic minimal hypersurfaces
| Autor: | De Philippis, Guido, De Rosa, Antonio, Li, Yangyang |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | In any closed smooth Riemannian manifold of dimension at least three, we use the min-max construction to find anisotropic minimal hyper-surfaces with respect to elliptic integrands, with a singular set of codimension~$2$ vanishing Hausdorff measure. In particular, in a closed $3$-manifold, we obtain a smooth anisotropic minimal surface. The critical step is to obtain a uniform upper bound for density ratios in the anisotropic min-max construction. This confirms a conjecture by Allard [Invent. Math., 1983]. Comment: 40 pages |
| Databáze: | arXiv |
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