Huhe Han

activity

20152024

most citedStrictly convex Wulff shapes and

C^{1}

convex integrands

7 citations · 12 across the 15 of their papers we have counts for

collaborators

15 papers

math.MG2024

From spherical separation center set to the upper and lower bound theorems

Huhe Han

In this paper, we provide the upper bound and the lower bound of the sum of the number of spherical face-partition pair of simple spherical polytope $P$ with $p$ facets.

math.MG2024

Approximation of spherical convex bodies of constant width $π /2$

Huhe Han

Let $C \subset S^{2}$ be a spherical convex body of constant width $τ$ . It is known that (i) if $τ < π /2$ then for any $ε > 0$ there exists a spherical convex body $C_\…

math.MG2023

Behavior of convex integrand at apex of its Wulff shape

Huhe Han

Let $γ : S^{n} \to R_{+}$ be a convex integrand and $W_{γ}$ be the Wulff shape of $γ$ . Apex point naturally arise in non-smooth Wulff shape, in particular, vertex of co…

math.MG2023

Self-dual polytope and self-dual smooth Wulff shape

Huhe Han

For any Wulff shape $W$ , its dual Wulff shape and spherical Wulff shape $W$ can be defined naturally. A self-dual Wulff shape is a Wulff shape equal…

math.MG2020★ 1 cited

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 $W_{1}, W_{2}$ of $S^{n}$ , the intersection $\mathcal{W}_1\cap…

math.MG2019

Constant diameter and constant width of spherical convex bodies

Huhe Han, Denghui Wu

In this paper we show that a spherical convex body $C$ is of constant diameter $τ$ if and only if $C$ is of constant width $τ$ , for $0 < τ < π$ . Moreover, some applications to Wulff sh…

math.GT2017★ 1 cited

Simultaneous smoothness and simultaneous stability of a $C^{\infty}$ strictly convex integrand and its dual

Erica Boizan Batista, Huhe Han, Takashi Nishimura

In this paper, we investigate simultaneous properties of a convex integrand $γ$ and its dual $δ$ . The main results are the following three. (1) For a $C^{\infty}$ convex integrand $γ…

math.MG2017

Maximum and minimum of support functions

Huhe Han

For given continuous functions $γ_{_{i}} : S^{n} \to R_{+}$ (where $i = 1, 2$ ), the functions $γ_{_{ma x}}$ and $γ_{_{min}}$ can be defined as natural way. In this paper,…

math.MG2016★ 1 cited

The Wulff construction for convex integrands

Huhe Han, Takashi Nishimura

For any given Wulff shape $W$ , we can define the unique continuous function $S^{n} \to R_{+}$ called convex integrand, denoted by $γ_{_{W}}$ . In this…

math.GT2016

Simultaneous stability of $C^{\infty}$ convex integrands and their duals

Erica Boizan Batista, Huhe Han, Takashi Nishimura

In this paper, the following three are shown. (1) For a $C^{\infty}$ convex integrand $γ : S^{n} \to R_{+}$ , its dual convex integrand $δ : S^{n} \to R_{+}$ is of class $C^\inf…

math.GT2016

Stability of $C^{\infty}$ convex integrands

Erica Boizan Batista, Huhe Han, Takashi Nishimura

In this paper, it is shown that the set consisting of stable convex integrands $S^{n} \to R_{+}$ is open and dense in the set consisting of $C^{\infty}$ convex integrands with re…

math.MG2015

Self-dual Wulff shapes and spherical convex bodies of constant width $π / 2$

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…

math.MG2015

Uniqueness of the surface energy density for a Wulff shape with $C^{1}$ boundary

Huhe Han, Takashi Nishimura

Let $γ : S^{n} \to R_{+}$ be a continuous function and let $W_{γ}$ be the Wulff shape associated with $γ$ . In this paper, we show that if the boundary of $W_{γ}$ …

math.MG2015★ 7 cited

Strictly convex Wulff shapes and $C^{1}$ 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 $C^{1}$ . Moreover, applications of this result are given.

math.MG2015★ 2 cited

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…

From spherical separation center set to the upper and lower bound theorems

Approximation of spherical convex bodies of constant width π/2

Behavior of convex integrand at apex of its Wulff shape

Self-dual polytope and self-dual smooth Wulff shape

Spherical Separation Theorem

Constant diameter and constant width of spherical convex bodies

Simultaneous smoothness and simultaneous stability of a C∞ strictly convex integrand and its dual

Maximum and minimum of support functions

The Wulff construction for convex integrands

Simultaneous stability of C∞ convex integrands and their duals

Stability of C∞ convex integrands

Self-dual Wulff shapes and spherical convex bodies of constant width π/2

Uniqueness of the surface energy density for a Wulff shape with C1 boundary

Strictly convex Wulff shapes and C1 convex integrands

The spherical dual transform is an isometry for spherical Wulff shapes

Approximation of spherical convex bodies of constant width $π /2$

Simultaneous smoothness and simultaneous stability of a $C^{\infty}$ strictly convex integrand and its dual

Simultaneous stability of $C^{\infty}$ convex integrands and their duals

Stability of $C^{\infty}$ convex integrands

Self-dual Wulff shapes and spherical convex bodies of constant width $π / 2$

Uniqueness of the surface energy density for a Wulff shape with $C^{1}$ boundary

Strictly convex Wulff shapes and $C^{1}$ convex integrands