关于ℝ³中各向异性伯恩斯坦问题的说明

Proceedings of the American Mathematical Society, Series B Pub Date : 2024-05-15 DOI:10.1090/bproc/214

César Rosales

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引用次数: 0

摘要

詹金斯证明[Arch. Rational Mech. Anal. 8 (1961), 181-206] R 3 {mathbb {R}}^3 中各向异性平均曲率消失的光滑全图一定是平面。通过使用校准论证和稳定性不等式，我们在此展示了这一结果的另一种自足证明，当各向异性平均曲率为常数时，它仍然有效。

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A note on the anisotropic Bernstein problem in ℝ³

It was proved by Jenkins [Arch. Rational Mech. Anal. 8 (1961), 181–206] that a smooth entire graph in R 3 {\mathbb {R}}^3 with vanishing anisotropic mean curvature must be a plane. By using a calibration argument and a stability inequality we show here a different self-contained proof of this result, which is still valid when the anisotropic mean curvature is constant.

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

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0.00%

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