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The space of solutions to the Hessian one equation in the finitely punctured plane

✍ Scribed by José A. Gálvez; Antonio Martínez; Pablo Mira

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
255 KB
Volume
84
Category
Article
ISSN
0021-7824

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✦ Synopsis

We construct the space of solutions to the elliptic Monge-Ampère equation det(D 2 φ) = 1 in the plane R 2 with n points removed. We show that, modulo equiaffine transformations and for n > 1, this space can be seen as an open subset of R 3n-4 , where the coordinates are described by the conformal equivalence classes of once punctured bounded domains in C of connectivity n -1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampère equation, and generalizes a theorem by K. Jörgens.

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