Abstract: We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same smooth cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that generically expanders with vanishing relative entropy are unique. This also implies that generically locally entropy minimizing expanders are unique. This is joint work with A. Deruelle.
Abstract: We will explain how to prove properness of a complete embedded minimal surface in Euclidean three-space, provided that the surface has finite genus and countably many limit ends (and possibly compact boundary).
This is joint work with William H. Meeks and Antonio Ros.
Abstract: I will survey the recent progress on the existence problem for minimal hypersurfaces and then point for some new directions. This is joint work with Fernando Marques.
Abstract: We give some existence and non-existence results for minimal annuli in H2xR whose data at infinity are given.