Variational problems connected with Monge-Ampere type operators

In this note we describe a geometric problem leading to Monge-Ampere type operators. Some variational problems and theorems on their solvability are formulated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 186–189, 1988.