The University of Dublin | Trinity College -- Ollscoil Átha Cliath | Coláiste na Tríonóide
Trinity's Access to Research Archive
Home :: Log In :: Submit :: Alerts ::

TARA >
School of Mathematics >
Pure & Applied Mathematics >
Pure & Applied Mathematics (Scholarly Publications) >

Please use this identifier to cite or link to this item: http://hdl.handle.net/2262/64093

Title: On Levi-flat hypersurfaces with prescribed boundary
Author: ZAITSEV, DMITRI
Sponsor: 
Name Grant Number
06/RFP/MAT018

Author's Homepage: http://people.tcd.ie/zaitsevd
Keywords: Levi-flat hypersurface
Complex Variables
Differential Geometry
Issue Date: 2010
Citation: Dolbeault, P., Tomassini, G., Zaitsev, D, On Levi-flat hypersurfaces with prescribed boundary, Pure and Applied Mathematics Quarterly, 6, 3, 2010, 725-753
Series/Report no.: Pure and Applied Mathematics Quarterly;6, 3
Abstract: We address the problem of existence and uniqueness of a Levi-flat hypersurface M in ℂn with prescribed compact boundary S for n ≥ 3. The situation for n ≥ 3 differs sharply from the well studied case n = 2. We first establish necessary conditions on S at both complex and CR points, needed for the existence of M. All CR points have to be nonminimal and all complex points have to be "flat". Then, adding a positivity condition at complex points, which is similar to the ellipticity for n = 2 and excluding the possibility of S to contain complex (n - 2)-dimensional submanifolds, we obtain a solution M to the above problem as a projection of a possibly singular Levi-flat hypersurface in ℝ × ℂn. It turns out that S has to be a topological sphere with two complex points and with compact CR orbits, also topological spheres, serving as boundaries of the (possibly singular) complex leaves of M. There are no more global assumptions on S like being contained in the boundary of a strongly pseudoconvex domain, as it was in case n = 2. Furthermore, we show in our situation that any other Levi-flat hypersurface with boundary S must coincide with the constructed solution.
Description: PUBLISHED
URI: http://hdl.handle.net/2262/64093
Related links: http://arxiv.org/abs/0904.0481
Appears in Collections:Pure & Applied Mathematics (Scholarly Publications)

Files in This Item:

File Description SizeFormat
levi.pdfPublished (author's copy) - Peer Reviewed298.3 kBAdobe PDFView/Open


This item is protected by original copyright


Please note: There is a known bug in some browsers that causes an error when a user tries to view large pdf file within the browser window. If you receive the message "The file is damaged and could not be repaired", please try one of the solutions linked below based on the browser you are using.

Items in TARA are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - Feedback