任意维数和余维数集合的积分Menger曲率
偏微分方程分析
2015-03-17 v6 度量几何
摘要
我们提出了n维欧氏空间中紧致m维集合的积分Menger曲率概念，并证明该量的有限性意味着该集合是C^{1,α}嵌入流形，其Hölder范数和映射大小仅依赖于曲率。我们发展了Strzelecki和von der Mosel [Adv. Math. 226(2011)]引入的思想，并采用类似策略证明我们的结果。
引用
@article{arxiv.1011.2008,
title = {Integral Menger curvature for sets of arbitrary dimension and codimension},
author = {Sławomir Kolasiński},
journal= {arXiv preprint arXiv:1011.2008},
year = {2015}
}
备注
This dissertation is not going to be published. The article "Geometric Sobolev-like embedding using high-dimensional Menger-like curvature" [arXiv:1205.4112] obsoletes my thesis. For any further reference one should use [arXiv:1205.4112] or its published version