A class of overdetermined systems defined by tableaux: involutiveness and Cauchy problem

This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by tableaux.Comment: 14 page

The mean curvature flow for isoparametric submanifolds

A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite time to a smooth submanifold of lower dimension. We also give a precise description of the collapsing.Comment: 24 pages, PDF fil