Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case

Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case

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Nikhil Savale, University of Cologne
IAS - Simonyi Hall Seminar Room SH-101

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case. A key role in all results is played by the presence of abnormal geodesics and represents the first such appearance of these in sub-Riemannian spectral geometry.