1 次谐函数的最小层叠和水平集

The Journal of Geometric Analysis Pub Date : 2024-08-08 DOI:10.1007/s12220-024-01758-8

Aidan Backus

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引用次数: 0

摘要

我们收集了有关极小层理正则性的若干结果，以及极小层理序列的各种收敛模式。然后，我们运用这一理论证明，如果一个函数的水平集是最小层叠，则该函数具有局部最小梯度（1 次谐波）；这解决了达斯卡洛普洛斯和乌伦贝克的一个未决问题。

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Minimal Laminations and Level Sets of 1-Harmonic Functions

We collect several results concerning regularity of minimal laminations, and governing the various modes of convergence for sequences of minimal laminations. We then apply this theory to prove that a function has locally least gradient (is 1-harmonic) iff its level sets are a minimal lamination; this resolves an open problem of Daskalopoulos and Uhlenbeck.

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The Journal of Geometric Analysis

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