17 citations · 20 across the 5 of their papers we have counts for
9 papers
A survey of closed self-shrinkers with symmetry
Gregory Drugan, Hojoo Lee, Xuan Hien Nguyen
In this paper, we survey known results on closed self-shrinkers for mean curvature flow and discuss techniques used in recent constructions of closed self-shrinkers with classical…
Shrinking doughnuts via variational methods
Gregory Drugan, Xuan Hien Nguyen
We use variational methods and a modified curvature flow to give an alternative proof of the existence of a self-shrinking torus under mean curvature flow. As a consequence of the…
Rotational symmetry of self-expanders to the inverse mean curvature flow with cylindrical ends
Gregory Drugan, Frederick Tsz-Ho Fong, Hojoo Lee
We show that any complete, immersed self-expander to the inverse mean curvature flow, which has one end asymptotic to a cylinder, or has two ends asymptotic to two coaxial cylinder…
Mean curvature flow of an entire graph evolving away from the heat flow
Gregory Drugan, Xuan Hien Nguyen
We present two initial graphs over the entire , for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flo…
Legendrian curve shortening flow in
Gregory Drugan, Weiyong He, Micah W. Warren
Motivated by Legendrian curve shortening flows in , we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and cu…
Solitons for the inverse mean curvature flow
Gregory Drugan, Hojoo Lee, Glen Wheeler
We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. In the case of one dimensional planar solitons, we explicitly classify all homothetic s…