Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening

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dc.creatorChéritat, Arnaud
dc.date2008-11-16
dc.date.accessioned2026-07-07T10:18:46Z
dc.date.available2026-07-07T10:18:46Z
dc.descriptionConsider the straightening phi of a Beltrami form that is constant on a square, with the corresponding ellipses having a vertical major axis, and null outside. A generalized Schwarz-Christoffel formula is used to express the inverse of phi. The formula is found by introducing an affine Riemann surface. This formula is used to draw on a computer the image of the square by phi, and practical aspects are discussed. The resulting shapes are shown for different values of the constant dilatation ratio of the ellipses (=major axis/minor axis). The limit when this ratio tends to infinity is surprising. A model of this limit is proposed, produced by an affine surface uniformization.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/0811.2601
dc.identifierhttp://arxiv.org/abs/0811.2601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174301
dc.subjectComplex Variables
dc.titleBeltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening
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