11 may 2006
Davide Vittone (S.N.S.)
on Thursday, 11 May, at 17:30
in ``Sala dei Seminari'' of the Mathematics Department, will speak of
"An intrinsic measure for submanifolds in stratified groups"
ABSTRACT We present the problem of finding the intrinsic sub-Riemannian measure ``naturally'' associated to a given submanifold of a stratified group. After a brief presentation of this setting, we will show some new results obtained in collaboration with V. Magnani. We introduce a ``local dimension'' (the so-called degree) for each point of a submanifold $\Sigma$ and show that the intrinsic tangent cone of $\Sigma$ is a subgroup at points of maximum degree. The negligibility of points with lower degree provides the intrinsic sub-Riemannian measure associated with $\Sigma$. We also provide the formula to compute the Hausdorff dimension of $\Sigma$ as the maximum degree of all points.