Methods and Applications of Analysis
Volume 25 (2018)
In Memory of Professor John N. Mather: Part 2 of 3
Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.
Limit of the Hausdorff distance for one-parameter families of Wulff shapes constructed by affine perturbations of dual Wulff shapes
Pages: 277 – 290
It is known that the Wulff construction is an isometry. In this paper we provide an alternative proof of this fact. Moreover, according to this result we investigate the limit of the Hausdorff distance for one-parameter families of Wulff shapes constructed by affine perturbations of dual Wulff shapes.
Wulff shape, Pompeiu–Hausdorff metric, maximum distance, dual Wulff shape
2010 Mathematics Subject Classification
47N10, 52A30, 82D25
The second author was partially supported by JSPS KAKENHI Grant Number JP17K05245.
Received 31 May 2018
Accepted 6 August 2018
Published 1 November 2019