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

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dc.creatorGalvez, Jose A.
dc.creatorMartinez, Antonio
dc.creatorMira, Pablo
dc.date2004-11-15
dc.date.accessioned2026-07-07T05:14:20Z
dc.date.available2026-07-07T05:14:20Z
dc.descriptionWe construct the space of solutions to the elliptic Monge-Ampere equation det(D^2 u)=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 the complex plane of connectivity n-1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampere equation, and generalizes a theorem by K. Jorgens.
dc.description14 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0411325
dc.identifierhttp://arxiv.org/abs/math/0411325
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73239
dc.subjectAnalysis of PDEs
dc.subject35J60;35J15
dc.titleThe space of solutions to the Hessian one equation in the finitely punctured plane
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