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. / <p>Funding by FMB, based at Uppsala University.</p>
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:miun-21641 |
| Date | January 2014 |
| Creators | Daghighi, Abtin |
| Publisher | Mittuniversitetet, Avdelningen för ämnesdidaktik och matematik, Sundsvall : Mid Sweden University |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Doctoral thesis, comprehensive summary, info:eu-repo/semantics/doctoralThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Mid Sweden University doctoral thesis, 1652-893X ; 183 |
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