2000/10/30 by D. Burns, Burns, D., Richard Hind +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #math.SG #msc:32Q28 #msc:32Q65 #msc:53D12
paper · pdf · doi:10.48550/arxiv.math/0010299
LaTeX2e file, 13 pages
arxiv created 2000/10/30 · arxiv updated 2009/11/30
A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex analysis, several authors have considered whether a given complex manifold can arise in more than one way from this construction. We show that given a compact M and a finite exhaustion, the underlying Riemannian structure is unique. The proof uses the technique of holomorphic disks spanning two exact Lagrangian submanifolds of the cotangent bundle of M, and Schwarz reflection.