arXiv subjects

Hyogo Shibahara

Publications and source records attributed to Hyogo Shibahara.

3 recordsLinked to original sources

arXiv2023

A $C^m$ Whitney Extension Theorem for Horizontal Curves in Free Step $2$ Carnot Groups

We establish a $C^m$ Whitney extension theorem for horizontal curves in free step~$2$ Carnot groups $\mathbb{G}_r$ for an arbitrary number of generators $r \geq 2$. This extends existing results in the Heisenberg group. New techniques include a quantitative linear dependence structure on jets on the horizontal layer, a discretization process to correct vertical areas, and studying the effect of unrelated vertical areas.

math.MG↗

arXiv2022

Some remarks on the Gehring-Hayman theorem

In this paper we provide new characterizations of the Gehring-Hayman theorem from the point of view of Gromov boundary and uniformity. We also determine the critical exponents for the uniformized space to be a uniform space in the case of the hyperbolic spaces, the model spaces $\mathbb{M}^κ_n$ of the sectional curvature $κ<0$ with the dimension $n \geq 2$ and hyperbolic fillings.

math.MG↗

arXiv2021

Gromov-Hausdorff distance with boundary and its application to Gromov hyperbolic spaces and uniform spaces

In this paper we introduce a notion of the Gromov-Hausdorff distance with boundary, denoted by $d_{GHB}$, to construct a framework of convergence of noncomplete metric spaces. We show that a class of bounded $A$-uniform spaces with diameter bounded from below is a complete metric space with respect to $d_{GHB}$. As an application we show the stability of Gromov hyperbolicity, roughly starlike property, uniformization, quasihyperbolization, and boundary of Gromov hyperbolic spaces under appropriate notions of convergence and assumptions.

math.MG↗