各向异性曲率测度与凸体的唯一性
度量几何
2022-04-15 v2 微分几何
摘要
我们证明，对于任意凸体 ，如果其第 阶各向异性曲率测度（对于 ）是 C 的各向异性周长的常数倍，则该凸体必定是一个经过缩放和平移的Wulff形状。这一结果推广了Schneider（1979）的一个定理，并解决了Andrews和Wei（2017）的一个猜想。
引用
@article{arxiv.2108.01476,
title = {Anisotropic curvature measures and uniqueness of convex bodies},
author = {Mario Santilli},
journal= {arXiv preprint arXiv:2108.01476},
year = {2022}
}
备注
This preprint is not going to be published, as a solution of the conjecture mentioned in the abstract is contained in Theorem 2.43 of "Daniel Hug. Measures, curvatures and currents in convex geometry. Habilitationsschrift, Albert-Ludwigs-Universitaet, Freiburg im Breisgau, December 1999. https://doi.org/10.6094/UNIFR/167349". This submission is superseded by arXiv:2204.04909