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Riemannian metrics and Laplacians for generalized smooth distributions.
- Source :
- Journal of Topology & Analysis; Jun2021, Vol. 13 Issue 2, p395-441, 47p
- Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- RIEMANNIAN metric
DIFFERENTIAL operators
CALCULUS
PSEUDODIFFERENTIAL operators
Subjects
Details
- Language :
- English
- ISSN :
- 17935253
- Volume :
- 13
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Topology & Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 151382710
- Full Text :
- https://doi.org/10.1142/S1793525320500168