Mean Curvature Flow and Bernstein-Calabi Results for Spacelike Graphs

Abstract

This is a survey of our work on spacelike graphic submanifolds in pseudo-Riemannian products, namely on Heinz-Chern and Bernstein-Calabi results and on the mean curvature flow, with applications to the homotopy of maps between Riemannian manifolds.

Contribution to the VIII International Colloquium on Differential Geometry, Santiago de Compostela, Spain, 7-11 July 2008, satellite event of the 5th European Congress of Mathematics