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Riemannian metrics and Laplacians for generalized smooth distributions
Authors
I. Androulidakis Kordyukov, Y.
Publication date
1 January 2021
Publisher
Abstract
We show that any generalized smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying manifold is compact, we show that it is essentially self-adjoint. Viewing this Laplacian in the longitudinal pseudodifferential calculus of the smallest singular foliation which includes the distribution, we prove hypoellipticity. © 2021 World Scientific Publishing Company
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Last time updated on 10/02/2023