Domination of geometric data sets is closed under box convergence, and limit formulas recover observable diameter and multi-directed separation after one-sided perturbations of mass parameters.
Pyramidal Compactification of Asymmetric Metric Measure Spaces via Adjoint Transport
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abstract
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 support. Motivated by the problem of determining the pyramid limits of beta measures on forward Funk balls, we construct a compact metric space of pyramids of qm-spaces. The associated-pyramid map from the concentration-distance space of qm-spaces into this compact space is a $1$-Lipschitz topological embedding with dense image. As a secondary result, we prove that the box-distance space of qm-spaces is complete and separable.
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math.MG 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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Extensions of One-Sided Box Geometry and Pyramid Invariants to gd-Sets and qm-Spaces
Domination of geometric data sets is closed under box convergence, and limit formulas recover observable diameter and multi-directed separation after one-sided perturbations of mass parameters.