Poisson geometry and deformation quantization near a pseudoconvex boundary

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dc.creatorLeichtnam, Eric
dc.creatorTang, Xiang
dc.creatorWeinstein, Alan
dc.date2006-03-14
dc.date.accessioned2026-07-07T07:06:53Z
dc.date.available2026-07-07T07:06:53Z
dc.descriptionLet X be a complex manifold with strongly pseudoconvex boundary M. If u is a defining function for M, then -log u is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form s = i \del \delbar(-log u) is a symplectic structure on the complement of M in a neighborhood in X of M; it blows up along M. The Poisson structure obtained by inverting s extends smoothly across M and determines a contact structure on M which is the same as the one induced by the complex structure. When M is compact, the Poisson structure near M is completely determined up to isomorphism by the contact structure on M. In addition, when -log u is plurisubharmonic throughout X, and X is compact, bidifferential operators constructed by Englis for the Berezin-Toeplitz deformation quantization of X are smooth up to the boundary. The proofs use a complex Lie algebroid determined by the CR structure on M, along with some ideas of Epstein, Melrose, and Mendoza concerning manifolds with contact boundary.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0603350
dc.identifierhttp://arxiv.org/abs/math/0603350
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110192
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.subject32T15; 53D10, 53D17
dc.titlePoisson geometry and deformation quantization near a pseudoconvex boundary
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