Minimal immersions in Finsler spaces

  • Minimale Immersionen in Finslerräumen

Overath, Patrick; von der Mosel, Heiko (Thesis advisor)

Aachen (2014)
Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2014

Abstract

The present thesis generalizes results established in [Souza,Tenenblat,2003], [Souza,Spruck,Tenenblat,2004] and [Cui,Shen,2009] on Finsler-minimal hypersurfaces in Finsler manifolds equipped with the Busemann-Hausdorff volume wherefrom the Finsler area derives. Therefore, a Finsler structure F the (m+1)-dimensional real vector space is assumed and some conditions involving the m-symmetrization of F are formulated to guarantee the ellipticity of the Finsler area. The present thesis generalizes especially Bernstein-type theorems of [Souza,Spruck,Tenenblat,2004] and [Cui,Shen,2009] beyond the class of (alpha,beta)-metrics. There are even many new results some of which with no direct counterpart in the aforementioned references. These results include existence and regularity of minimizers, removability of singularities, enclosure theorems, isoperimetric inequalities and curvature estimates for Finsler-minimal hypersurfaces.

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