Methods and Applications of Analysis

Volume 25 (2018)

Number 4

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

DOI: https://dx.doi.org/10.4310/MAA.2018.v25.n4.a1

Authors

Huhe Han (College of Science, Northwest Agriculture and Forestry University, Yangling, Shaanxi Province, China)

Takashi Nishimura (Research Group of Mathematical Sciences, Research Institute of Environment and Information Sciences, Yokohama National University, Yokohama, Japan)

Abstract

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.

Keywords

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