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The spherical dual transform is an isometry for spherical Wulff shapes

Volume 245 / 2019

Huhe Han, Takashi Nishimura Studia Mathematica 245 (2019), 201-211 MSC: Primary 47N10; Secondary 52A30, 82D25. DOI: 10.4064/sm8406-9-2016 Published online: 6 July 2018

Abstract

A spherical Wulff shape is the spherical counterpart of a Wulff shape which is the well-known geometric model of a crystal at equilibrium introduced by G. Wulff in 1901. Just as a Wulff shape, each spherical Wulff shape has its unique dual. The spherical dual transform for spherical Wulff shapes is the mapping which maps a spherical Wulff shape to its spherical dual Wulff shape. In this paper, it is shown that the spherical dual transform for spherical Wulff shapes is an isometry with respect to the Pompeiu–Hausdorff metric.

Authors

  • Huhe HanCollege of Sciences
    Northwest Agriculture and Forestry University
    712100 Yangling, China
    e-mail
  • Takashi NishimuraResearch Institute of Environment
    and Information Sciences
    Yokohama National University
    240-8501 Yokohama, Japan
    e-mail

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