卵形体第二基本形式面积泛函研究
微分几何
2009-09-18 v3
摘要
欧氏空间中超曲面第二基本形式面积泛函的变分表达式涉及所谓的“第二基本形式的平均曲率”。本文给出了若干涉及第二基本形式平均曲率的（超）球面的新特征性质。特别是，证明了在各种约束条件下，球面是第二基本形式面积泛函的临界点的唯一卵形体。
引用
@article{arxiv.0709.1644,
title = {On the Area Functional of the Second Fundamental Form of Ovaloids},
author = {Steven Verpoort},
journal= {arXiv preprint arXiv:0709.1644},
year = {2009}
}
备注
13 pages. (v2: As compared to a previous version of this article, which was entitled "The Mean Curvature of the Second Fundamental Form of an Ovaloid", there have been made substantial changes especially to the latter part of the article.) (v3: Reference to the work of M. Wiehe has been added.) Published version available here: http://www.emis.de/journals/MPRIA/100152.html