# An intrinsic measure for submanifolds in stratified groups

## Davide Vittone (Dip. Matematica, Univ. di Padova)

created by magnani on 10 May 2006

11 may 2006

Abstract.

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.

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