New examples of Moser–Bernstein type problems for some nonlinear elliptic partial differential equations arising in geometry

Abstract

A family of nonlinear partial differential equations of divergence form is considered. Each one is the Euler–Lagrange equation of a natural Riemaniann variational problem of geometric interest. New uniqueness results for the entire solutions of these equations on a parabolic Riemaniann manifold of arbitrary dimension are given. In particular, several Moser–Bernstein type theorems are proved.