How Willmore Submanifolds are used in Machine Learning part1 – Monodeep Mukherjee

Photo by Jude Infantini on UnsplashRigidity Result for Four Dimensional Willmore Submanifolds with Boundary(arXiv)Author : Peter Olamide OlanipekunAbstract : We set up a rigidity outcome for the important factors, with boundary, of a 4 dimensional Willmore power. These important factors fulfill a 4-Willmore equation which is a sixth order nonlinear elliptic partial differential equation. We set up a number of curvature estimates and show that 4 dimensional Willmore submanifold with completely geodesic boundary situation are umbilic2. Willmore submanifolds in the unit sphere by way of isoparametric capabilities(arXiv)Author : Yuquan XieAbstract : This paper is a continuation of [TY12] and [QTY13]. We present that each focal submanifolds of every isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore.

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