ON S. BERNSTEIN'S THEOREM ON SURFACES z(x, y) OF NONPOSITIVE CURVATURE
نویسنده
چکیده
That this estimate of the order of magnitude at infinity cannot be essentially improved is shown by examples of the form z=f(x) —g(y), /">0, g">0, where/ and g can be chosen such that the order is just 0(r). A still open question is whether z(x, y) can or cannot be o(r) along a special sequence of radii r —>». In proving the theorem we shall, essentially, follow Bernstein's original arguments. For the sake of completeness the arguments will be repeated.
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