Search results for "Conformal map"

showing 5 items of 125 documents

Geodesic flow of the averaged controlled Kepler equation

2008

A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyGeodesicGeneral MathematicsCut locusConformal map02 engineering and technologyKepler's equationFundamental theorem of Riemannian geometry01 natural sciencesConvexityIntrinsic metricsymbols.namesake020901 industrial engineering & automationSingularity0101 mathematicsorbit transferMathematicsApplied Mathematics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]cut and conjugate lociRiemannian metrics49K15 70Q05symbols[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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Canal foliations of S 3

2012

The goal of the article is to classify foliations of S3 by regular canal surfaces, that is envelopes of one-parameter families of spheres which are immersed surfaces. We will add some extra information when the leaves are “surfaces of revolution” in a conformal sense.

foliationGeneral Mathematics53A30Foliation (geology)Conformal mapGeometryMathematics::Differential GeometrySurface of revolution53C12MathematicsComputingMethodologies_COMPUTERGRAPHICScanal surface
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Lectures on quasiconformal and quasisymmetric mappings

2009

quasiconformal mappingskvasikonforminen kartoitusquasisymmetric mappingskvasisymmetrinen kartoitus
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Weighted Hardy Spaces of Quasiconformal Mappings

2019

We establish a weighted version of the $H^p$-theory of quasiconformal mappings.

radial maximal functionsfunktioteoriaHardy spacesMathematics - Complex Variablesmodulus estimateHardyn avaruudetFOS: Mathematicsquasiconformal mappingGeometry and TopologyComplex Variables (math.CV)nontangential30C65The Journal of Geometric Analysis
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Openness and Discreteness

2013

The aim of this chapter is to study conditions under which a mapping of finite distortion is open (maps open sets to open sets) and discrete (preimage of each point is a discrete set).

symbols.namesakeDirac measureDistortionMathematical analysisOpen setsymbolsOpenness to experiencePoint (geometry)Conformal mapDiscrete setNonlinear elasticityMathematics
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