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arXiv · 1705.10117

Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals

M. G. Delgadino·F. Maggi·C. Mihaila·R. Neumayer
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Abstract

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems.

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M. G. Delgadino, F. Maggi, C. Mihaila, R. Neumayer. 2017-05-29. Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals. https://doi.org/10.1007/s00205-018-1267-8

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