Self-Shrinkers to the Mean Curvature Flow asymptotic to Isoparametric Cones
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Date
2016-07-19
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Johns Hopkins University
Abstract
We record work done by the author joint with Professor Joel Spruck[9] on constructing self-shrinking end to the mean curvature flow asymptotic to an isoparametric cone C and lying outside of C. We call a cone C in Rn+1 an isoparametric cone if C is the cone over a compact embedded isoparametric hypersurface Γ ⊂ Sn. The theory of isoparametric hypersurface is extremely rich and there are infinitely many distinct classes of examples, each with infinitely many members.
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Keywords
Mean Curvature Flow, Self-Shrinker, Isoparametric Hypersurface, Degenerate Singular Differential Equation, Differential Geometry