Total mean curvature surfaces in the product space S^n x R and applications

Abstract

The total mean curvature functional for submanifolds into the Riemannian product space S^n × R is considered and its first variational formula is presented. Later on, two second order differential operators are defined and a nice integral inequality relating both of them is proved. Finally we prove our main result: an integral inequality for closed stationary H-surfaces in S^n × R, characterizing the cases where the equality is attained.