Preprints and Recent Publications

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The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations
by Yan Yan Li and Louis Nirenberg

This interesting paper studies the structure of the singular set of the distance function to the boundary of a bounded domain provided with a Finsler metric.


Minimalité de sous-variétés totalement géodésiques en géométrie finslerienne
by Gautier Berck

This paper proves that if the Holmes-Thompson definition of volume is used, then totally geodesic submanifolds of Finsler spaces extremize the area functional. This is a fundamental result in the theory of areas on Finsler spaces and serves to separate the Holmes-Thompson definition from the Busemann definition (the Hausdorff measure)---its closest competitor---for which this result does not hold (Álvarez and Berck). The paper also contains a simple and elegant formalism for doing calculus of variations with differential k-densities.