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Abstract.It is proved that the negatively curved set M on a nonparametric surface M of constant mean curvature in 3 must extend to the boundary M, if M is nonempty. For M parametric, if M is compactly included in the interior of M, then M is at least as large as an extremal domain. The results imply certain convexity results on elliptic partial differential equations. Secondorder calculus of variation...
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