2008/06/07 by Giuseppe Tomassini, Tomassini, Giuseppe, Sergio Venturini +1
Mathematics · #32C09 #32F45 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32C09 #msc:32F45
paper · pdf · doi:10.48550/arxiv.0806.1275
27 pages
arxiv created 2008/06/07 · openalex publication_date 2008/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An analytic pair of dimension n and center V is a pair (V, M) where M is a complex manifold of (complex) dimension n and V is a closed totally real analytic submanifold of dimension n. To an analytic pair (V, M) we associate the class of the functions u from M to a positive bounded interval which are plurisubharmonic in M and such that u(p) = 0 for each p in V. If the class admits a maximal function u, the triple (V, M, u) is said to be a maximal plurisubharmonic model. After defining a pseudo-metric E(V,M) on the center V of an analytic pair (V, M) we prove (see Theorem 4.1, Theorem 5.1) that maximal plurisubharmonic models provide a natural generalization of the Monge-Ampere models introduced by Lempert and Szoke in [16].