A generalization of Rado's Theorem for almost graphical boundaries

Brian Dean; Giuseppe Tinaglia

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A generalization of Rado's Theorem for almost graphical boundaries

Brian Dean·Giuseppe Tinaglia

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Abstract

In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is "almost graphical" in some sense, that the surface must be graphical once we move sufficiently far from the boundary.

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Brian Dean, Giuseppe Tinaglia. 2005-02-25. A generalization of Rado's Theorem for almost graphical boundaries. https://arxiv.org/abs/math/0502551

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