HARMONIC ANALYSIS MEETS CRITICAL KNOTS. CRITICAL POINTS OF THE MOBIUS ENERGY ARE SMOOTH
HARMONIC ANALYSIS MEETS CRITICAL KNOTS. CRITICAL POINTS OF THE MOBIUS ENERGY ARE SMOOTH
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DOI：
10.1090/tran/6603
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发表时间：
2016-09-01
影响因子：
1.3
通讯作者：
Schikorra, Armin
中科院分区：
文献类型：
--
作者：
Blatt, Simon;Reiter, Philipp;Schikorra, Armin
受曲线上均匀分布电荷的库仑势的启发，Jun O'Hara 引入并研究了第一个几何结能量，即莫比乌斯能量。我们证明该莫比乌斯能量的每条临界曲线都是 C 无穷大类，从而扩展了 Freedman、He 和 Wang 的相应结果，以获得莫比乌斯能量的最小化。与 Freedman、He 和 Wang 使用的技术相比，我们的方法不使用能量的莫比乌斯不变性，而是依赖于纯粹的解析方法，该方法源于欧拉-朗朗日方程与单位正切的半调和映射方程的形式相似性。
Motivated by the Coulomb potential of an equidistributed charge on a curve, Jun O'Hara introduced and investigated the first geometric knot energy, the Mobius energy. We prove that every critical curve of this Mobius energy is of class C-infinity and thus extend the corresponding result due to Freedman, He, and Wang for minimizers of the Mobius energy.In contrast to the techniques used by Freedman, He, and Wang, our methods do to not use the Mobius invariance of the energy, but rely on purely analytic methods motivated from a formal similarity of the Euler-Langrange equation to the half harmonic map equation for the unit tangent.