Research profile
Works on rotational symmetry & warped products, self-shrinkers & translators and inverse mean curvature flow.
Elsewhere arXiv listing
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How many of these papers carry each topic, among the topics most particular to them. Tags are assigned automatically, so they point to a subject rather than judge the work.
FlowsSpecial solutionsGeometry & analysisConnections
| Topic | 2016 | 2017 |
|---|---|---|
| All papers | 2 | 1 |
| Rotational symmetry & warped products | 2 | 1 |
| Self-shrinkers & translators | 2 | 1 |
| Inverse mean curvature flow | 2 | |
| Numerics & visualization | 1 | |
| Other curvature flows | 2 | |
| Stability & uniqueness | 1 | 1 |
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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.
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.
We use the weighted Hsiung-Minkowski integral formulas and Brendle's inequality to show new rigidity results. First, we prove Alexandrov type results for closed embedded hypersurfaces with radially symmetric higher order mean curvature in a large class of Riemannian warped product manifolds, including the Schwarzschild and Reissner-Nordström spaces, where the Alexandrov reflection principle is not available. Second, we prove that, in Euclidean space, the only closed immersed self-expanding solitons to the weighted generalized inverse curvature flow of codimension one are round hyperspheres.
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.
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NP-RC-856171 is Hojoo Lee's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.
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