Propagation of low regularity for solutions of nonlinear PDEs on a   Riemannian manifold with a sub-Laplacian structure
  Following \cite{B2}, we introduce a notion of para-products associated to a semi-group. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-laplacian structure. Our main result is a paralinearization theorem in a non-euclidean framework, with an application to the propagation of regularity for some nonlinear PDEs. 
Fr\'ed\'eric Bernicot and Yannick Sire
math.AP