A sharp Bernstein-type theorem for entire minimal graphs

Alberto Farina

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arXiv · 1707.04113

A sharp Bernstein-type theorem for entire minimal graphs

Alberto Farina

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Abstract

We consider entire solutions $u$ to the minimal surface equation in $R^N$, with $ N\ge8,$ and we prove the following sharp result : if $N-7$ partial derivatives $ \frac{\partial u }{\partial {x_j}}$ are bounded on one side (not necessarily the same), then $u$ is necessarily an affine function.

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Alberto Farina. 2017-07-13. A sharp Bernstein-type theorem for entire minimal graphs. https://arxiv.org/abs/1707.04113

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