In this paper we study the lower semicontinuous envelope with respect to the -topology of a class of isotropic functionals with linear growth defined on mappings from the -dimensional ball into that are constrained to take values into a smooth submanifold of .
In this paper we study the lower semicontinuous envelope with respect to the L1-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into that are constrained to take values into a smooth submanifold of .
We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.
A flag on a manifold is an increasing sequence of foliations on this manifold, where for each , . The aim of this paper is to etablish that any flag of riemannian foliations
Nous étudions les notions de relevés formels de champs de tenseurs, d’opérateurs multidifférentiels, de formalités et de star produits de à et d’une variété à son fibré tangent .
This short note completes the results of [3] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [3] can be characterized in a completely algebraic way, even without any continuity assumption on the operations.