Monge-Ampere foliations with singularities at the boundary of strongly convex domains
F Bracci, G Patrizio - Mathematische Annalen, 2005 - Springer
F Bracci, G Patrizio
Mathematische Annalen, 2005•SpringerLet be a bounded strongly convex domain with smooth boundary. We consider a Monge-
Ampère 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.
Ampère 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.
Abstract
Let be a bounded strongly convex domain with smooth boundary. We consider a Monge-Ampère 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.
Springer
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