Universite catholique de louvain

The talk will discuss the variationnal problem on finite

dimensional normed spaces and Finsler manifolds.

We first review different notions of ellipticity (convexity) for

parametric integrands (densities) on normed spaces and compare them with

different minimality properties of affine subspaces. Special attention will

be given to Busemann and Holmes-Thompson k-area. If time permits, we will

then present the first variation formula on Finsler manifolds and exhibit a

class of minimal submanifolds.