Metrics of constant curvature on a Riemann surface with two corners on the boundary

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dc.creatorJost, Juergen
dc.creatorWang, Guofang
dc.creatorZhou, Chunqin
dc.date2007-12-19
dc.date.accessioned2026-07-07T08:50:20Z
dc.date.available2026-07-07T08:50:20Z
dc.descriptionWe use PDE methods as developed for the Liouville equation to study the existence of conformal metrics with prescribed singularities on surfaces with boundary, the boundary condition being constant geodesic curvature. Our first result shows that a disk with two corners admits a conformal metric with constant Gauss curvature and constant geodesic curvature on its boundary if and only if the two corners have the same angle. In fact, we can classify all the solutions in a more general situation, that of the 2-sphere cut by two planes.
dc.descriptionto appear in Annales de l'IHP-ANL
dc.identifierhttps://arxiv.org/abs/0712.3162
dc.identifierhttp://arxiv.org/abs/0712.3162
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144571
dc.subjectDifferential Geometry
dc.subject58J32;58J05;35J65
dc.titleMetrics of constant curvature on a Riemann surface with two corners on the boundary
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