Maximal Plurisubharmonic Models
نویسنده
چکیده
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 U (V,M) of the functions u : M → [0,π/4[ which are plurisubharmonic in M and such that u(p)= 0 for each p ∈ V . If U (V,M) 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 [16].
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