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

This paper considers minimal surfaces in and prove that if a connected surface M in is minimal with respect to both the Busemann-Hausdorff volume form and the Holmes-Thompson volume form, then up to a parallel translation of , M is either a piece of plane or a piece of helicoid which is generated by...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2007-06, Vol.31 (4), p.375-384
Main Author: Wu, Bing Ye
Format: Article
Language:English
Subjects:
Euclidean space
Geometry
Mathematical models
Minimal surfaces
Minkowski space
Studies
Theory
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Summary:This paper considers minimal surfaces in and prove that if a connected surface M in is minimal with respect to both the Busemann-Hausdorff volume form and the Holmes-Thompson volume form, then up to a parallel translation of , M is either a piece of plane or a piece of helicoid which is generated by lines screwing about the x 3-axis.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-006-9046-4