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

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

We contemplate Finsler areas with a Randers metric F = α + β, at the three-d actual vector house, the place α is the Euclidean metric and β is a 1-form with norm b, zero ≤ b < 1. through the use of the thought of suggest curvature for immersions in Finsler areas, brought via 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 end up that it's an elliptic equation of suggest curvature kind. Then the Bernstein variety theorem and different homes, akin to the nonexistence of remoted singularities, of the options of this equation persist with from the speculation developped by means of L. Simon. For b ≥ 1/, the differential equation isn't really elliptic. in addition, for each b, 1/ < b < 1 we offer strategies, which describe minimum cones, with an remoted singularity on the beginning.

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