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Potential Theory on Minimal Hypersurfaces II: Hardy Structures and Schrödinger Operators
Potential Analysis ( IF 1.1 ) Pub Date : 2020-08-18 , DOI: 10.1007/s11118-020-09869-x
Joachim Lohkamp

Area minimizing hypersurfaces and, more generally, almost minimizing hypersurfaces frequently occur in geometry, dynamics and physics. A central problem is that a general (almost) minimizing hypersurface H contains a complicated singular set Σ. Nevertheless, we manage to develop a detailed potential theory on H ∖Σ applicable to large classes of linear elliptic second order operators. We even get a fine control over their analysis near Σ. This is Part 2 of this two parts work.



中文翻译:

最小超曲面的势能理论II:Hardy结构和Schrödinger算符

在几何学,动力学和物理学中,经常出现使超曲面最小化的区域,更普遍地,几乎使超曲面最小化的区域。一个中心问题是一般的(几乎)最小化超曲面H包含复杂的奇异集合Σ。然而,我们设法开发出一种适用于大型线性椭圆二阶算子的H ∖Σ势能理论。我们甚至可以很好地控制他们在Σ附近的分析。这是这两个部分的第2部分。

更新日期:2020-08-18
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