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- W1567103681 abstract "We study the problem of finding a minimal graph with prescribed boundary data in arbitrary dimension and codimension. Existence, uniqueness, stability and regularity are treated. We first present the well-known results for codimension one: Jenkins-Serrin's existence theorem, convexity properties of the area which give uniqueness and stability and De Giorgi's theorem for regularity. In higher codimension we first discuss the counterexamples of Lawson and Osserman. Then we present the recent results of Mu-Tao Wang: we use the mean curvature flow to show existence for small boundary data and we prove a new Bernstein theorem (also due to Mu-Tao Wang) which holds for every area-decreasing minimal graph. We finally deduce from the Bernstein theorem that an area-decreasing minimal graph is always smooth." @default.
- W1567103681 created "2016-06-24" @default.
- W1567103681 creator A5083968975 @default.
- W1567103681 date "2004-11-26" @default.
- W1567103681 modified "2023-09-27" @default.
- W1567103681 title "The non-parametric problem of Plateau in arbitrary codimension" @default.
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- W1567103681 hasPublicationYear "2004" @default.
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