Splitting and Bernstein theorems for CMC graphs under Ricci lower bounds

Abstract: In this talk, we study constant mean curvature (CMC) graphs defined over domains of a complete manifold $M$ with Ricci curvature bounded from below. In particular, we show that complete manifolds with non-negative Ricci curvature do not support entire, positive minimal graphs. We also prove a splitting theorem for capillary graphs defined on domains $\Omega \subset M$, that is, for CMC graphs with overdetermined boundary conditions on $\Omega$. All of the results hinge on new, global gradient estimates for CMC graphs on possibly unbounded domains of $M$.

PortugueseMathematics

Audience: general audience

Seminários de Matemática da UFPB