Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies
Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies
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DOI：
10.1002/cpa.21713
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发表时间：
2018-06-01
影响因子：
3
通讯作者：
Ghiraldin, Francesco
中科院分区：
文献类型：
--
作者：
De Philippis, Guido;De Rosa, Antonio;Ghiraldin, Francesco
我们将Allard著名的可纠性定理推广到关于各向异性被积函数具有局部有界第一变差的变量集的情形。特别地，我们给出了一个关于被积函数的充要条件，从而得到了具有局部有界第一变差和正d维密度的每一个d维变量的可正性。在余维1中，这一条件等价于被积函数关于切平面的严格凸性。(C)2017威利期刊公司。
We extend Allard's celebrated rectifiability theorem to the setting of varifolds with locally bounded first variation with respect to an anisotropic integrand. In particular, we identify a sufficient and necessary condition on the integrand to obtain the rectifiability of every d-dimensional varifold with locally bounded first variation and positive d-dimensional density. In codimension 1, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane. (C) 2017 Wiley Periodicals, Inc.