Propagation of singularities for subelliptic wave equations

Cyril Letrouit

doi:10.1007/s00220-022-04415-9

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arXiv · 2106.07216

Propagation of singularities for subelliptic wave equations

Cyril Letrouit

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Abstract

H{\"o}rmander's propagation of singularities theorem does not fully describe the propagation of singularities in subelliptic wave equations, due to the existence of doubly characteristic points. In the present work, building upon a visionary conference paper by R. Melrose \cite{Mel86}, we prove that singularities of subelliptic wave equations only propagate along null-bicharacteristics and abnormal extremals, which are well-known curves in optimal control theory. As a consequence, we characterize the singular support of subelliptic wave kernels outside the diagonal. These results show that abnormal extremals play an important role in the classical-quantum correspondence between sub-Riemannian geometry and sub-Laplacians.

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Cyril Letrouit. 2021-06-14. Propagation of singularities for subelliptic wave equations. https://doi.org/10.1007/s00220-022-04415-9

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