A local rigidity theorem for minimal surfaces in Minkowski 3-space of Randers type期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A local rigidity theorem for minimal surfaces in Minkowski 3-space of Randers type

Authors:	Bing Ye Wu

Institution:	(1) Department of Mathematics, Minjiang University, Fuzhou, Fujian, 350108, China

Abstract:	Let $(\mathbb{R}^3,\widetilde{F}_b)$ be a Minkowski 3-space of Randers type with $\widetilde{F}_b=\widetilde{\alpha}+\widetilde{\beta}$ , where $\widetilde{\alpha}$ is the Euclidean metric and $\widetilde{\beta}=bdx^3,0 < b < 1$ . We consider minimal surfaces in $(\mathbb{R}^3,\widetilde{F}_b)$ and prove that if a connected surface M in $\mathbb{R}^3$ is minimal with respect to both the Busemann–Hausdorff volume form and the Holmes–Thompson volume form, then up to a parallel translation of $\mathbb{R}^3$ , M is either a piece of plane or a piece of helicoid which is generated by lines screwing about the x ³-axis.

Keywords:	Minkowski space of Randers type Mean curvature BH-minimal HT-minimal
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