Abstract: A regular subriemannian manifold M carries a geometric hypoelliptic operator, the intrinsic sublaplacian. Due to the degeneracy of the operator symbol, effects occur in the geometry and analysis of these operators that have no equivalent in Riemannian geometry. During the last decades inverse spectral problems in subriemannian geometry have been studied by various authors. Typical approaches are based on the analysis of the induced subriemannian heat or wave equation.
The first part of the talk provides a short introduction to subriemannian geometry. We mention some applications and define the induced hypoelliptic operators (sublaplacian). In the special case of Euclidean spheres and of so-called H-type foliations, we discuss the spectral theory of such operators and, in particular, the geometric content of the subriemannian spectrum. This talk is based on joint work with A. Laaroussi, I. Markina and S. Vega-Molino.
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