15 citations · 38 across the 29 of their papers we have counts for
7 papers · 1 filter
Spherical Separation Theorem
Huhe Han, Takashi Nishimura
In this paper, it is shown that for any two non-empty closed (resp., open) and spherical convex subsets of , the intersection $\mathcal{W}_1\cap…
The Wulff construction for convex integrands
Huhe Han, Takashi Nishimura
For any given Wulff shape , we can define the unique continuous function called convex integrand, denoted by . In this…
Self-dual Wulff shapes and spherical convex bodies of constant width
Huhe Han, Takashi Nishimura
For any Wulff shape, its dual Wulff shape is naturally defined. A self-dual Wulff shape is a Wulff shape equaling its dual Wulff shape exactly. In this paper, it is shown that a Wu…
Uniqueness of the surface energy density for a Wulff shape with boundary
Huhe Han, Takashi Nishimura
Let be a continuous function and let be the Wulff shape associated with . In this paper, we show that if the boundary of …
Strictly convex Wulff shapes and convex integrands
Huhe Han, Takashi Nishimura
In this paper, it is shown that a Wulff shape is strictly convex if and only if its convex integrand is of class . Moreover, applications of this result are given.
The spherical dual transform is an isometry for spherical Wulff shapes
Huhe Han, Takashi Nishimura
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. As same as…