Regularity and uniqueness-related properties of solutions with respect to locally integrable structures
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
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.
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 183
Maximum principle, hypocomplexity, locally integrable structure, hypoanalytic structure, weak pseudoconcavity, uniqueness, CR functions
IdentifiersURN: urn:nbn:se:miun:diva-21641ISBN: 978-91-87557-44-6OAI: oai:DiVA.org:miun-21641DiVA: diva2:713025
2014-05-21, O102, Mid Sweden University, Sundsvall, 10:15 (English)
Leiterer, Jürgen, Professor
Porten, Egmont, ProfessorKiselman, Christer, ProfessorBorell, Stefan, Senior Lecturer
Funding by FMB, based at Uppsala University.2014-04-242014-03-292015-09-17Bibliographically approved