arXiv subjects

Micah W. Warren

Publications and source records attributed to Micah W. Warren.

2 recordsLinked to original sources

arXiv2018

Ricci Curvature and the Manifold Learning Problem

Consider a sample of $n$ points taken i.i.d from a submanifold $Σ$ of Euclidean space. We show that there is a way to estimate the Ricci curvature of $Σ$ with respect to the induced metric from the sample. Our method is grounded in the notions of Carré du Champ for diffusion semi-groups, the theory of Empirical processes and local Principal Component Analysis.

math.DG↗

arXiv2015

Legendrian curve shortening flow in $\mathbb{R}^{3}$

Motivated by Legendrian curve shortening flows in $\mathbb{R}^{3}$, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time.

math.DG↗