By Souza M., Spruck J., Tenenblat K.

We ponder Finsler areas with a Randers metric F = α + β, at the third-dimensional genuine vector house, the place α is the Euclidean metric and β is a 1-form with norm b, zero ≤ b < 1. by utilizing the thought of suggest curvature for immersions in Finsler areas, brought by way of Z. Shen, we receive the partial differential equation that characterizes the minimum surfaces that are graphs of capabilities. for every b, zero ≤ b < 1/, we turn out that it's an elliptic equation of suggest curvature kind. Then the Bernstein sort theorem and different homes, resembling the nonexistence of remoted singularities, of the options of this equation keep on with from the speculation developped by way of L. Simon. For b ≥ 1/, the differential equation isn't really elliptic. additionally, for each b, 1/ < b < 1 we offer ideas, which describe minimum cones, with an remoted singularity on the beginning.

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A Bernstein type theorem on a Randers space by Souza M., Spruck J., Tenenblat K.

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