Constant principal strain mappings on 2-manifolds

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dc.contributor.authorChuaqui, M
dc.contributor.authorGevirtz, J
dc.date.accessioned2025-01-21T01:31:40Z
dc.date.available2025-01-21T01:31:40Z
dc.date.issued2000
dc.description.abstractWe study mappings between Riemannian 2-manifolds which have constant principal stretching factors (cps-mappings). Such mappings f can be described in terms of the relationship between the geodesic curvature of the curves of principal strain at p and that of their images at f (p). In the context of local coordinates this relationship takes the form of a nonlinear hyperbolic system, the blow-up properties of which depend on the Gaussian curvatures of the two manifolds. We use the theory of such systems to study global existence when both manifolds are the hyperbolic plane H-2 and obtain a simple description of all cps-mappings of H-2 onto itself. We also obtain a distortion result for disks in H-2 as well as some nonexistence results for cps-mappings of the Euclidean plane onto certain classes of manifolds. In addition, our treatment of cps-mappings in H-2 yields, virtually as a corollary, a generalization of a theorem of Epstein to the effect that a curve in hyperbolic n-space whose geodesic curvature is bounded by 1 must be simple.
dc.fuente.origenWOS
dc.identifier.issn0036-1410
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/97118
dc.identifier.wosidWOS:000166214100002
dc.issue.numero4
dc.language.isoen
dc.pagina.final759
dc.pagina.inicio734
dc.revistaSiam journal on mathematical analysis
dc.rightsacceso restringido
dc.subjectconstant principal strains
dc.subjecthyperbolic system
dc.subjecthyperbolic plane
dc.titleConstant principal strain mappings on 2-manifolds
dc.typeartículo
dc.volumen32
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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