Jocel Faustino Norberto de Oliveira

Modified mean curvature flow of graphs in Riemannian manifolds

We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for this extrinsic flow with smooth initial data.