Calculus of Variations and Geometric Measure Theory
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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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