Affiliation:
1. Scuola Normale Superiore, Piazza dei Cavalieri, 7, I-56126 Pisa, Italy
2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40127 Bologna, Italy
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 [Formula: see text] of the functions u : M → [0, π/4] which are plurisubharmonic in M and such that u(p) = 0 for each p ∈ V. If [Formula: see text] 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].
Publisher
World Scientific Pub Co Pte Lt
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