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Annals of Global Analysis and Geometry

, Volume 48, Issue 4, pp 397–422 | Cite as

On minimal immersions in Finsler space

  • Patrick Overath
  • Heiko von der MoselEmail author
Article

Abstract

We explore a connection between the Finslerian area functional and well-investigated Cartan functionals to prove new Bernstein theorems, uniqueness and removability results for Finsler-minimal graphs, as well as enclosure theorems and isoperimetric inequalities for minimal immersions in Finsler spaces. In addition, we establish the existence of smooth Finsler-minimal immersions spanning given extreme or graph-like boundary contours.

Keywords

Finsler-minimal immersions Cartan functionals Spherical Radon transform 

Mathematics Subject Classification

44A12 49Q05 49Q10 53A35 53B40 53C60 

Notes

Acknowledgments

Substantial parts of this work are contained in the first author’s thesis which was partially supported by DFG grant no. Mo 966/3-1,2, and moreover by the Excellence Initiative of the German Federal and State Governments. Moreover, the second author would like to express his gratitude to Professor Seiki Nishikawa for inviting him to Tohoku University at Sendai, Japan, to give a series of talks on this line of research.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für MathematikRWTH Aachen UniversityAachenGermany

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