对偶 Orlicz-Brunn-Minkowski 理论
度量几何
2015-06-10 v1 微分几何
摘要
本文引入了针对星形集的对偶 Orlicz-Brunn-Minkowski 理论。提出了两个或多个星形集的径向 Orlicz 加法，并建立了相应的对偶 Orlicz-Brunn-Minkowski 不等式。基于两个星形集的径向 Orlicz 线性组合，推导了对偶 Orlicz 混合体积的公式，并证明了对应的对偶 Orlicz-Minkowski 不等式。所证明的不等式作为特例，给出了 B"{o}r"{o}czky、Lutwak、Yang 和 Zhang 提出的猜想 log-Brunn-Minkowski 不等式和 log-Minkowski 不等式的精确对偶形式。此外，还引入了一种称为径向 -加法的新星形集加法，并证明了其与径向 Orlicz 加法的关系。
关键词
引用
@article{arxiv.1407.7311,
title = {The Dual Orlicz-Brunn-Minkowski Theory},
author = {Richard J. Gardner and Daniel Hug and Wolfgang Weil and Deping Ye},
journal= {arXiv preprint arXiv:1407.7311},
year = {2015}
}
备注
The present paper is a combination of a manuscript by the first three authors dated May 21, 2013, and the preprint arXiv:1404.6991 written independently by the fourth author. Special cases of some of the results in the present paper were obtained independently in Chapter 5 of the thesis of B. Zhu (see Appendix for a brief description of the difference between them)