Discrepancy and isotopy for manifold approximations
Date of Completion
January 2009
Keywords
Applied Mathematics|Computer Science
Degree
Ph.D.
Abstract
This thesis examines manifold approximation, specifically in one and two dimensions, by constructing an efficient set of sample points. These points are chosen so that, they are uniformly distributed with respect to the curvature of the manifold. We utilize the tool of discrepancy to measure how uniformly distributed the sample sets are. We are able to prove geometric bounds on the distance and tangential deviation of the approximant. This framework in turn allows us to demonstrate conditions upon which we can guarantee the approximant is ambient isotopic to the manifold. ^
Recommended Citation
Miller, Lance Edward, "Discrepancy and isotopy for manifold approximations" (2009). Doctoral Dissertations. AAI3388413.
https://digitalcommons.lib.uconn.edu/dissertations/AAI3388413