Modified mean curvature flow of graphs in riemannian manifolds

Abstract

In this thesis we will prove the existence of solution to the problem of modified mean curvature flow with smooth initial data. For this purpose we will need a priori estimates to guarantee the use of the theory of parabolic differential equations, more precisely the quasilinear theory. Our main result is obtained for a smooth, n-dimensional, complete, non-compact manifold with pole. The ambient manifold is a warped-product endowed with a Killing field which defines the warping function. Some geometrical considerations are made in order to encompass particular cases. Evolution equations are calculated in order to be used in the estimates.