https://neckpinch.com/authors/zihan-hans-liu/New arXiv papers by Zihan Hans Liu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1603.06539/arxiv:1603.06539Mon, 21 Mar 2016 00:00:00 GMTZihan Hans Liu — We introduce a notion of index for shrinkers of the mean curvature flow. We then prove a gap theorem for the index of rotationally symmetric immersed shrinkers in R^3, namely, that such shrinkers have index at least 3, unless they are one of the stable ones: the sphere, the cylinder, or the plane. We also provide a generalization of the result to higher dimensions.Mean curvature flowRicci solitonsRotational symmetry & warped products