Pretangent spaces with nonpositive and nonnegative Aleksandrov curvature
Viktoriia Bilet, Oleksiy Dovgoshey
TL;DR
This paper investigates conditions that determine when pretangent spaces of metric spaces exhibit nonpositive or nonnegative Aleksandrov curvature, and explores their infinitesimal structure, especially in Busemann convex cases.
Contribution
It provides new criteria for curvature properties of pretangent spaces and describes their infinitesimal structure in Busemann convex metric spaces.
Findings
Conditions for nonpositive Aleksandrov curvature in pretangent spaces
Conditions for nonnegative Aleksandrov curvature in pretangent spaces
Description of infinitesimal structure in Busemann convex spaces
Abstract
We find conditions under which the pretangent spaces to general metric spaces have the nonpositive Aleksandrov curvature or nonnegative one. The infinitesimal structure of general metric cpaces with Busemann convex pretangent spaces is also described.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds