An existence theorem for stationary discs in almost complex manifolds

2005/02/06 by Andrea Spiro, Spiro, Andrea, Alexandre Sukhov +1
Mathematics · #32H02 #53C15 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Symplectic Geometry (math.SG) #math.CV #math.SG #msc:32H02 #msc:53C15

paper · pdf · doi:10.48550/arxiv.math/0502121

18 pages

arxiv created 2005/02/06 · openalex publication_date 2005/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An existence theorem for stationary discs of strongly pseudoconvex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces there exists a unique stationary disc passing through that point and tangent to the given vector.

Related

• Foliations by stationary disks of almost complex domains
• Riemann maps in almost complex manifolds
• Filling hypersurfaces by discs in almost complex manifolds of dimension 2
• Discs and boundary uniqueness for psh functions on almost complex manifolds
• Homogeneous almost complex manifolds and their compact quotients