Finite Quasihypermetric Spaces
Peter Nickolas, Reinhard Wolf

TL;DR
This paper investigates the geometric properties and maximal subspaces of finite quasihypermetric metric spaces, focusing on the constant M(X) and L^1-embeddability, extending previous work in distance geometry.
Contribution
It introduces new insights into the structure of finite quasihypermetric spaces, especially regarding maximal strictly quasihypermetric subspaces and L^1-embeddability.
Findings
Characterization of M(X) in finite quasihypermetric spaces
Identification of maximal strictly quasihypermetric subspaces
Conditions for L^1-embeddability of finite metric spaces
Abstract
Let be a compact metric space and let denote the space of all finite signed Borel measures on . Define by , and set , where ranges over the collection of measures in of total mass 1. The space is \emph{quasihypermetric} if for all measures in of total mass 0 and is \emph{strictly quasihypermetric} if in addition the equality holds amongst measures of mass 0 only for the zero measure. This paper explores the constant and other geometric aspects of in the case when the space is finite, focusing first on the significance of the maximal strictly quasihypermetric subspaces of a given finite quasihypermetric space and second on the class of finite metric spaces…
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Analytic and geometric function theory
