From the 2 of 6 linked papers with an AI index.
6 papers
Extensions of One-Sided Box Geometry and Pyramid Invariants to gd-Sets and qm-Spaces
Shigeaki Yokota
Domination of gd-sets, the relation recording which function family approximates which, is closed under box convergence. More generally, approximate 1-Lipschitz maps on asymptotica…
Pyramidal Compactification of Asymmetric Metric Measure Spaces via Adjoint Transport
Shigeaki Yokota
A quasi-metric measure space (qm-space) is a set with a directed distance whose symmetrization is a complete separable metric, together with a Borel probability measure of full sup…
Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions
Shigeaki Yokota
The paper investigates radial measures in high‑dimensional hyperbolic space, showing that shell concentration alone does not determine the limiting metric‑measure pyramid because a…
Poincaré Beta Balls: Radial Laws, Shell Transforms, and Phase Diagram
Shigeaki Yokota
The paper analyzes how a Euclidean beta-type radial measure concentrates on high‑dimensional Poincaré balls and how hyperbolic distance amplifies the remaining spread, identifying…
Geometry of Geometric Data Set II: Pyramid
Shigeaki Yokota
The observable distance based on measure concentration and the box distance based on collapsing theory are extended to geometric data sets introduced by…
Geometry of Geometric Data Set I
Shigeaki Yokota
Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable…