Uniform a priori estimates for a class of horizontal minimal equations

Abstract

Abstract. In the product space H n × R, we obtain uniform a priori C 0 horizontal length estimates, uniform a priori C 1 boundary gradient estimates, as well as uniform modulus of continuity, for a class of horizontal minimal equations. In two independent variables, we derive a certain uniform global a priori C 1 estimates and we infer an existence result.

Maximum principle and symmetry for minimal hypersurfaces in H^nxR

“…Finally we prove an Asymptotic Theorem (Theorem 4.7), that implies the following non-existence result. There is no horizontal minimal graph over a bounded strictly convex domain, see [10,Equation (3)], given by a positive function g continuous up to the boundary, taking zero boundary value data (Remark 4.9). ACKNOWLEDGEMENTS.…”