Measurability of classes of Lipschitz manifolds with respect to Borel -algebra of Vietoris topology
Measure extension for a piecewise invariant map
Measures on bundles and Trundles of measures
Measures representable as -dimensional Hausdorff measures
Menger curvature and rectifiability.
Mesures de Hausdorff et théorie de Perron-Frobenius des matrices non-négatives
Nous étudions des sous-ensembles parfaits de dont la structure dépend d’une matrice primitive à coefficients entiers . La dimension de Hausdorff d’un tel ensemble “fractal” s’exprime en fonction de la valeur propre réelle maximale de sa matrice associée. Nous utilisons le théorème de Perron-Frobenius pour calculer la valeur exacte (qui est finie et non-nulle) de la mesure de Hausdorff de cet ensemble, et nous montrons à quelle condition (géométrique) cette valeur est maximale.
Mesures spéciales dans l’espace
Mesures sur le cercle et convexes du plan
Minimizing movements for dislocation dynamics with a mean curvature term
We prove existence of minimizing movements for the dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity solutions of the corresponding level-set equation. We also prove the consistency of this approach, by showing that any minimizing movement coincides with the smooth evolution...
Misura di Hausdorff e misure approssimanti
Misure approssimanti ed insiemi ad ampiezza costante
Multifractals and projections.
In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.