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MAXIMAL PLURISUBHARMONIC MODELS
https://doi.org/10.1142/S0129167X09005856Cited by:1 (Source: Crossref)
Abstract
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 ⊂ M is a closed totally real analytic submanifold of dimension n. To an analytic pair (V, M) we associate the class 
of the functions u : M → [0, π/4] which are plurisubharmonic in M and such that u(p) = 0 for each p ∈ V. If 
admits a maximal function u, the triple (V, M, u) is said to be a maximal plurisubharmonic model. After defining a pseudo-metric EV, 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–Ampère models introduced by Lempert and Szöke in [18].
AMSC: Primary 32F45, Primary 32C09, Secondary 32Q45, Secondary 32T35
