Coarse intrinsic and extrinsic curvature in riemannian geometry
File(s)
Author(s)
Petko, Benedikt
Type
Thesis
Abstract
This work comprises several extensions to Ollivier’s coarse curvature within the domain of Riemannian geometry. We address the extension to weighted Riemannian manifolds by local weighted test measures, introduce a notion of coarse extrinsic curvature of Riemannian submanifolds of Euclidean spaces and study the coarse Ricci curvature of noisy submanifolds. We complement our results with applications to the problem of convergence of coarse curvature of geometric graphs and point clouds in the infinite sample limit in these extended settings.
Version
Open Access
Date Issued
2024-04-08
Date Awarded
01/06/2024
License URL
Advisor
Li, Xue-Mei
Hairer, Martin
Arnaudon, Marc
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/S023925/1
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)