内蕴平坦距离的性质
微分几何
2015-06-18 v5 度量几何
摘要
本文探讨了内蕴平坦收敛的各种性质。我们引入了切片填充体积和区间切片填充体积，并探讨了这些概念与四面体性质以及内蕴平坦收敛下点的消失之间的关系。我们证明了两个新的 Gromov-Hausdorff 和内蕴平坦紧致性定理，包括四面体紧致性定理。本文的大部分工作建立在 Ambrosio-Kirchheim 切片定理与改编版 Gromov 填充体积相结合的基础之上。
引用
@article{arxiv.1210.3895,
title = {Properties of the Intrinsic Flat Distance},
author = {J. Portegies and C. Sormani},
journal= {arXiv preprint arXiv:1210.3895},
year = {2015}
}
备注
V1-V2: by Sormani included F to GH Conv Thm, Arz-Asc Thms and BW Thms that were then simplified and moved to arXiv:1402.6066 and also an incomplete proof of the Tetrahedral Compactness Thm. V3: has a new coauthor Portegies and new Section 3. V4: new sections 4 and 5. V5: added new Appendix