A sharp lower bound on the mean curvature integral with critical power for integral varifolds
Abstract
Part I Weakly differentiable functions Part II PDEs on varifolds 15 Sobolev spaces ... 75 16 Preliminaries ... 82 17 Maximum estimates ... 86 18 Second order flatness of Lebesgue spaces for integral varifolds with subcritical integrability of the mean curvature ... 94 19 Second order differentiability of the support of integral varifolds with critical integrability of the mean curvature ... 100 20 Harnack inequality ... 108 Part III The generalised Gauss map 21 Points of finite lower density ... 118 22 Points of infinite density ... 130 23 Area formula for the generalised Gauss map ... 137 24 A sharp lower bound on the mean curvature integral with critical power for integral varifolds ... 138 Appendix A Monotonicity identity ... 139 B An observation concerning the Lusin property ... 140
Keywords
Cite
@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}
}
Comments
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