Foliations by stationary disks of almost complex domains

2009/05/12 by Giorgio Patrizio, Patrizio, Giorgio, Andrea Spiro +1
Mathematics · #32G05. #32H40 #32Q60 #32Q65 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32G05. #msc:32H40 #msc:32Q60 #msc:32Q65

paper · pdf · doi:10.48550/arxiv.0905.1905

22 pages

arxiv created 2009/05/12 · openalex publication_date 2009/05/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of existence of stationary disks for domains in almost complex manifolds. As a consequence of our results, we prove that any almost complex domains which is a small deformations of a strictly linearly convex domain D ⊂ Cⁿ with standard complex structure admits a singular foliation by stationary disks passing through any given internal point. Similar results are given for foliation by stationary disks through a given boundary point

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