[Cover page]
The distance function to the boundary, Finsler geometry, and the singular set
of viscosity solutions of some Hamilton-Jacobi equations
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
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.
by Yan Yan Li and Louis Nirenberg
by Gautier Berck