积分变流形上带临界幂的平均曲率积分的尖锐下界
微分几何
2024-07-25 v2
摘要
第一部分 弱可微函数 第二部分 变流形上的偏微分方程 15 Sobolev空间 ... 75 16 预备知识 ... 82 17 极大值估计 ... 86 18 平均曲率次临界可积的积分变流形Lebesgue空间的二阶平坦性 ... 94 19 平均曲率临界可积的积分变流形支撑的二阶可微性 ... 100 20 Harnack不等式 ... 108 第三部分 广义Gauss映射 21 有限下密度点 ... 118 22 无穷密度点 ... 130 23 广义Gauss映射的面积公式 ... 137 24 积分变流形上带临界幂的平均曲率积分的尖锐下界 ... 138 附录A 单调性恒等式 ... 139 B 关于Lusin性质的一个观察 ... 140
引用
@article{arxiv.2310.01754,
title = {A sharp lower bound on the mean curvature integral with critical power for integral varifolds},
author = {Ulrich Menne},
journal= {arXiv preprint arXiv:2310.01754},
year = {2024}
}
备注
v1: manuscript dated 2014. Complete proofs, few reader guidance, 24 chapters, 1 appendix, 144 pages. Part I (Chapters 1-14) is published in arXiv:1411.3287; Chapter 15 is published as part of arXiv:1509.01178; some material of Chapter 19 is included in arXiv:1603.08587; other chapters shall be generalised (with collaborators) and published elsewhere. v2: 2012 note on Lusin property new Appendix B