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Regularity and uniqueness-related properties of solutions with respect to locally integrable structures
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.ORCID iD: 0000-0001-7488-8004
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We prove that a smooth generic embedded CR submanifold of C^n obeys the maximum principle for continuous CR functions if and only if it is weakly 1-concave. The proof of the maximum principle in the original manuscript has later been generalized to embedded weakly q-concave CR submanifolds of certain complex manifolds. We give a generalization of a known result regarding automatic smoothness of solutions to the homogeneous problem for the tangential CR vector fields given local holomorphic extension. This generalization ensures that a given locally integrable structure is hypocomplex at the origin if and only if it does not allow solutions near the origin which cannot be represented by a smooth function near the origin. We give a sufficient condition under which it holds true that if a smooth CR function f on a smooth generic embedded CR submanifold, M, of C^n, vanishes to infinite order along a C^infty-smooth curve  \gamma in M, then f vanishes on an M-neighborhood of \gamma. We prove a local maximum principle for certain locally integrable structures.

Place, publisher, year, edition, pages
Sundsvall: Mid Sweden University , 2014. , 145 p.
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 183
Keyword [en]
Maximum principle, hypocomplexity, locally integrable structure, hypoanalytic structure, weak pseudoconcavity, uniqueness, CR functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-21641ISBN: 978-91-87557-44-6 (print)OAI: oai:DiVA.org:miun-21641DiVA: diva2:713025
Public defence
2014-05-21, O102, Mid Sweden University, Sundsvall, 10:15 (English)
Opponent
Supervisors
Note

Funding  by FMB, based at Uppsala University.

Available from: 2014-04-24 Created: 2014-03-29 Last updated: 2015-09-17Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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