Estimates for solutions of quasilinear elliptic equations connected with problems of geometry “in the large”

The following questions are presented in this paper.
1. A geometric method for obtaining two-sided estimates for general quasilinear elliptic equations and its applications to problems of the calculus of variations and the problem of recovering a hypersurface from its mean curvature in spaces of constant curvature.
2. Estimates of the modulus of the gradient for a hypersurface with boundary in a Riemannian space by means of its mean curvature and the metric tensor of the space.
3. Estimates of the modulus of the gradient of a hypersurface depending on the distance of a point from the boundary and its mean curvature in Euclidean space.
Estimates of these three types are of independent interest and play a fundamental role in the proofs of existence theorems for a hypersurface with prescribed mean curvature in Riemannian spaces.
Bibliography: 3 titles.