On The Regularity Of The Composition Of Diffeomorphisms
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On the Regularity of the Composition of Diffeomorphisms
Author: H. Inci
language: en
Publisher: American Mathematical Soc.
Release Date: 2013-10-23
For M a closed manifold or the Euclidean space Rn we present a detailed proof of regularity properties of the composition of Hs-regular diffeomorphisms of M for s > 12dimM+1.
Spectra of Symmetrized Shuffling Operators
Author: Victor Reiner
language: en
Publisher: American Mathematical Soc.
Release Date: 2014-03-05
For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of O -noninversions of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.
Cartesian Currents in the Calculus of Variations II
Author: Mariano Giaquinta
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
Non-scalar variational problems appear in different fields. In geometry, for in stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite complicated phenomena. Typically one is interested in finding energy minimizing representatives in homology or homotopy classes of maps, minimizers with prescribed topological singularities, topological charges, stable deformations i. e. minimizers in classes of diffeomorphisms or extremal fields. In the last two or three decades there has been growing interest, knowledge, and understanding of the general theory for this kind of problems, often referred to as geometric variational problems. Due to the lack of a regularity theory in the non scalar case, in contrast to the scalar one - or in other words to the occurrence of singularities in vector valued minimizers, often related with concentration phenomena for the energy density - and because of the particular relevance of those singularities for the problem being considered the question of singling out a weak formulation, or completely understanding the significance of various weak formulations becames non trivial.