https://neckpinch.com/authors/gregory-drugan/New arXiv papers by Gregory Drugan, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1708.09113/arxiv:1708.09113Wed, 30 Aug 2017 00:00:00 GMTGregory 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 rotational symmetry. We also propose new existence and uniqueness problems for closed self-shrinkers with bi-rotational symmetry and provide numerical evidence for the existence of new examples.Mean curvature flowSelf-shrinkers & translatorsStability & uniquenessRotational symmetry & warped productsNumerics & visualization https://neckpinch.com/papers/1708.08808/arxiv:1708.08808Tue, 29 Aug 2017 00:00:00 GMTGregory 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 proof, we establish an upper bound for the weighted energy of our shrinking doughnuts.Mean curvature flowOther curvature flowsSelf-shrinkers & translators https://neckpinch.com/papers/1608.02137/arxiv:1608.02137Sat, 06 Aug 2016 00:00:00 GMTGregory 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 cylinders, must be rotationally symmetric.Mean curvature flowOther curvature flowsInverse mean curvature flowSelf-shrinkers & translatorsRotational symmetry & warped products