3 papers
math.MG2023
A Whitney Extension Theorem for Horizontal Curves in Free Step Carnot Groups
Hyogo Shibahara
We establish a Whitney extension theorem for horizontal curves in free step~ Carnot groups for an arbitrary number of generators . This extends ex…
math.MG2022
Some remarks on the Gehring-Hayman theorem
Sari Rogovin, Hyogo Shibahara, Qingshan Zhou
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…
math.MG2021
Gromov-Hausdorff distance with boundary and its application to Gromov hyperbolic spaces and uniform spaces
Hyogo Shibahara
In this paper we introduce a notion of the Gromov-Hausdorff distance with boundary, denoted by , to construct a framework of convergence of noncomplete metric spaces. We s…