Geodesic
The spherical dual transform is an isometry for spherical Wulff shapes
Huhe Han1 ; Takashi Nishimura2
1 College of Sciences Northwest Agriculture and Forestry University 712100 Yangling, China
2 Research Institute of Environment and Information Sciences Yokohama National University 240-8501 Yokohama, Japan
Studia Mathematica, Tome 245 (2019) no. 3, pp. 201-211

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm8406-9-2016
Keywords: spherical wulff shape spherical counterpart wulff shape which well known geometric model crystal equilibrium introduced nbsp wulff just wulff shape each spherical wulff shape has its unique dual spherical dual transform spherical wulff shapes mapping which maps spherical wulff shape its spherical dual wulff shape paper shown spherical dual transform spherical wulff shapes isometry respect pompeiu hausdorff metric

Huhe Han 1 ; Takashi Nishimura 2

1 College of Sciences Northwest Agriculture and Forestry University 712100 Yangling, China
2 Research Institute of Environment and Information Sciences Yokohama National University 240-8501 Yokohama, Japan 
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Huhe Han; Takashi Nishimura. The spherical dual transform is an isometry for spherical Wulff shapes. Studia Mathematica, Tome 245 (2019) no. 3, pp. 201-211. doi: 10.4064/sm8406-9-2016

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