Let D subset of C-N be a bounded strongly convex domain with smooth boundary. We consider a Monge-Ampere type equation in D with a simple pole at the boundary. Using the Lempert foliation of D in extremal discs, we construct a solution u whose level sets are boundaries of horospheres. Among other things, we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution.

Bracci, F., Patrizio, G. (2005). Monge-Ampere foliations with singularities at the boundary of strongly convex domains. MATHEMATISCHE ANNALEN, 332(3), 499-522 [10.1007/s00208-005-0633-7].

Monge-Ampere foliations with singularities at the boundary of strongly convex domains

BRACCI, FILIPPO;
2005-01-01

Abstract

Let D subset of C-N be a bounded strongly convex domain with smooth boundary. We consider a Monge-Ampere type equation in D with a simple pole at the boundary. Using the Lempert foliation of D in extremal discs, we construct a solution u whose level sets are boundaries of horospheres. Among other things, we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution.
2005
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
PLURICOMPLEX POISSON KERNEL; HOROSPHERES; MONGE-AMPERE EQUATION
Bracci, F., Patrizio, G. (2005). Monge-Ampere foliations with singularities at the boundary of strongly convex domains. MATHEMATISCHE ANNALEN, 332(3), 499-522 [10.1007/s00208-005-0633-7].
Bracci, F; Patrizio, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/36531
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