Fatou’s theorem and minimal graphs. (English) Zbl 1207.53007
Summary: We extend a recent result of Collin-Rosenberg (a solution to the minimal surface equation in the Euclidean disc has radial limits almost everywhere) to a large class of differential operators in divergence form. Moreover, we construct an example (in the spirit of P. Collin and H. Rosenberg [Asymptotic values of minimal graphs in a disc, preprint. Available at: http://people.math.jussieu.fr/~rosen/Pascalharold]) of a minimal graph in \(\mathbb M^2 \times \mathbb R\), where \(\mathbb M^2\) is a Hadamard surface, over a geodesic disc which has finite radial limits in a measure zero set.
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
References:
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