Hilbert Volume in Metric Spaces
Misha Gromov
TL;DR
This paper introduces a new concept of Hilbertian n-volume in metric spaces, incorporating Besicovitch-type inequalities, aiming to aid in the study of singular spaces with positive scalar curvature.
Contribution
It defines a novel Hilbert volume in metric spaces with built-in inequalities, providing a new tool for analyzing singular spaces with curvature constraints.
Findings
Defined Hilbertian n-volume in metric spaces
Established Besicovitch-type inequalities for these volumes
Potential applications to singular spaces with positive scalar curvature
Abstract
We introduce a notion of Hilbertian n-volume in metric spaces with Besicovitch-type inequalities built-in into the definitions. which, ultimately, may turn useful for an approach to singular spaces with positive scalar curvature
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds