Non-Hilbertian tangents to Hilbertian spaces
Danka Lu\v{c}i\'c, Enrico Pasqualetto, Tapio Rajala
TL;DR
This paper presents examples of metric measure spaces that are infinitesimally Hilbertian but have tangents that are not, challenging assumptions about tangent space properties.
Contribution
It provides the first known examples of such spaces, revealing new complexities in the structure of metric measure spaces.
Findings
Existence of spaces with non-Hilbertian tangents
Counterexamples to previous conjectures
Insights into tangent space properties
Abstract
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
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.