A note on an overdetermined problem for minimal surface equation

Author:

Cui Qing

Abstract

We show in this short note an overdetermined problem for minimal surface equation, which is defined over a domain with connected boundary, has a solution if and only if the domain is either the complement of a round disk or a half plane. Equivalently, we show that a minimal graph with connected zero boundary and makes a constant angle at all boundary points with a plane is a part of a catenoid or a half-plane.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference18 articles.

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4. The Calabi-Yau conjectures for embedded surfaces;Colding, Tobias H.;Ann. of Math. (2),2008

5. Serrin’s overdetermined problem and constant mean curvature surfaces;Del Pino, Manuel;Duke Math. J.,2015

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