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Questions about the behavior of the mean curvature of surfaces given in the form of graph Xn+1 = f(x) over an arbitrary domain Ωin ℝn are considered. It is proved, for example, that if mean curvature H is a continuously monotonically increasing function of coordinates xn+1 in ℝn+1, then the following assertions are fulfilled: a) if Ω = ℝn, then H = 0, that is, the graph is a minimal surface; b) if ∂Ω ≠ ø, then $$\mathop {sup}\limits_{x \in \Omega } |H(f(x))| \cdot dist(x;\partial \Omega ) \leqslant 1$$ is true. Different special cases of Ω are considered, for which exact values of the constant on the right-hand side of (*) are obtained.

Some estimates of the mean curvature of nonparametric surfaces given over domains inR n