各向异性的Michael-Simon不等式
The anisotropic Michael-Simon inequality
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中文总结 AI 辅助
本文证明了任意维数和余维数varifolds的各向异性Michael-Simon不等式，结合相关定理给出超曲面正则性，还得出varifolds的密度界与紧性性质，证明依赖投影方法及消失质量猜想的解决。
中文摘要 AI 辅助
我们针对任意维数和余维数的varifolds（可变曲面），证明了关于各向异性能量的Michael-Simon不等式。结合Allard的各向异性正则性定理，该结果给出了所有维数下具有有界各向异性平均曲率的超曲面的正则性。利用De Philippis和Pigati的结果，这还意味着具有一致有界各向异性第一变分的可求积varifolds的密度界和紧性性质。该证明依赖于各向异性应力测度的投影方法，以及Gennaioli和Rindler最近对消失质量猜想的解决。
英文摘要
We prove a Michael-Simon inequality for varifolds of every dimension and codimension with respect to anisotropic energies. In particular, this resolves the problem for every convex even hypersurface anisotropy and, using work of Allard, yields the regularity of hypersurfaces with bounded anisotropic mean curvature in every dimension. By the results of De Philippis and Pigati, it also implies density bounds and compactness properties for rectifiable varifolds with uniformly bounded anisotropic first variation. The proof relies on a projection method for anisotropic stress measures as well as the recent resolution of the vanishing mass conjecture by Gennaioli and Rindler.
发表机构
- MIT（麻省理工学院）
- Columbia University（哥伦比亚大学）
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