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Riemannian metrics and Laplacians for generalized smooth distributions.

Authors :
Androulidakis, Iakovos
Kordyukov, Yuri
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]

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