Search results for "RIEMANN"

showing 10 items of 254 documents

Heisenberg quasiregular ellipticity

2016

Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold $M$ to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group $\mathbb{H}$. As an application, we show that a link complement $S^3\backslash L$ has a sub-Riemannian metric admitting such a mapping only if $L$ is empty, the unknot or Hopf link. In the converse direction, if $L$ is empty, a specific unknot or Hopf link, we construct a quasiregular mapping from $\mathbb{H}$ to $S^3\backslash L$. The main result is obtained by translating a growth condition on $\pi_1(M)$ into the existence of a supersolution to the $4$-harmonic…

Pure mathematicsGeneral MathematicsSobolev–Poincaré inequality01 natural sciences3-sphereMathematics - Geometric TopologyMathematics - Metric GeometryEuclidean geometryHeisenberg groupFOS: Mathematicssub-Riemannian manifold0101 mathematicsComplex Variables (math.CV)topologiaUnknotLink (knot theory)Complement (set theory)MathematicsMathematics::Complex VariablesMathematics - Complex Variablescapacity010102 general mathematicsta111Hopf linkGeometric Topology (math.GT)Metric Geometry (math.MG)quasiregular mappingisoperimetric inequality3-sphereHopf linkcontact manifoldlink complementpotentiaaliteoriaMathematics::Differential GeometryIsoperimetric inequalitymonistot
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A metric characterization of Carnot groups

2013

We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.

Pure mathematicsGeodesicGeneral MathematicsApplied MathematicsMathematical analysisMetric Geometry (math.MG)Characterization (mathematics)symbols.namesakeMathematics - Metric GeometryHomogeneousCarnot groupsMetric (mathematics)symbolsFOS: MathematicsMathematics (all)Mathematics::Metric GeometryMathematics::Differential GeometrySubRiemannian geometryCarnot cycleCarnot groups; SubRiemannian geometry; Mathematics (all); Applied MathematicsAxiomMathematics
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The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces

1997

AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.

Pure mathematicsGeodesictube53C21.Mathematical analysisGeodesic mapgeodesic balltotally geodesic submanifold.53C35Computational Theory and MathematicsSymmetric spaceTotally geodesicMathematics::Differential GeometryGeometry and TopologyCompact Riemannian symmetric spaceminimal focal distancerestricted rootsExponential map (Riemannian geometry)injectivity radiusAnalysisMathematicsDifferential Geometry and its Applications
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A new full descriptive characterization of Denjoy-Perron integral

1995

It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.

Pure mathematicsHenstock–Kurzweil integralMathematical analysisMeasure (physics)Riemann integralFunction (mathematics)Absolute continuitysymbols.namesakesymbolsAlmost everywhereGeometry and TopologyDaniell integralDifferentiable functionAnalysisMathematics
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Large-x Analysis of an Operator-Valued Riemann–Hilbert Problem

2015

International audience; The purpose of this paper is to push forward the theory of operator-valued Riemann-Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method a la Deift-Zhou. In this paper, we demonstrate that the operator-valued Riemann-Hilbert problem arising in the characterization of so-called c-shifted integrable integral operators allows one to extract the large-x asymptotics of the Fredholm determinant associated with such operators.

Pure mathematicsIntegrable systemNonlinear schrodinger-equationMathematics::Complex VariablesGeneral Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSIS[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Fredholm determinantImpenetrable bose-gas[ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA][MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]01 natural sciencessymbols.namesakeRiemann hypothesisOperator (computer programming)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesHilbert's problemssymbolsMethod of steepest descentRiemann–Hilbert problem010307 mathematical physics0101 mathematicsMathematics
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Kurzweil-Henstock type integration on Banach spaces

2004

In this paper properties of Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrals for vector-valued functions are studied. In particular, the absolute integrability for Kurzweil-Henstock integrable functions is characterized and a Kurzweil-Henstock version of the Vitali Theorem for Pettis integrable functions is given.

Pure mathematicsIntegrable systemequiintegrabilityInfinite-dimensional vector functionMathematical analysisBanach spaceRiemann–Stieltjes integralType (model theory)Infinite-dimensional holomorphyKurzweil-Henstock integral28B0526A39Pettis integralGeometry and TopologyDaniell integralLp spaceAnalysisMathematics
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Feuilletages Riemanniens singuliers

2006

Abstract We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

Pure mathematicsMathematical analysisGeneral MedicineRiemannian geometryFundamental theorem of Riemannian geometryPseudo-Riemannian manifoldLevi-Civita connectionsymbols.namesakesymbolsMinimal volumeMathematics::Differential GeometryExponential map (Riemannian geometry)Ricci curvatureScalar curvatureMathematicsComptes Rendus Mathematique
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La topologie à l'infini des variétés à géométrie bornée et croissance linéaire

1997

Abstract We study the topology at infinity of a non compact riemannian manifold with bounded geometry and linear growth-type.

Pure mathematicsMathematics(all)General Mathematicsmedia_common.quotation_subjectBounded functionApplied MathematicsMathematical analysisMathematics::Differential GeometryRiemannian manifoldInfinityTopology (chemistry)media_commonMathematicsJournal de Mathématiques Pures et Appliquées
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Recurrence and genericity

2003

We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative diffeomorphisms are transitive. Nous montrons un lemme de connexion C^1 pour les pseudo-orbites des diffeomorphismes des varietes compactes. Nous explorons alors les consequences pour les diffeomorphismes C^1-generiques. Par exemple, les diffeomorphismes conservatifs C^1-generiques sont transitifs.

Pure mathematicsMathematics::Dynamical SystemsRiemann manifold[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciences37C05 37C20FOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsDynamical system (definition)Mathematics::Symplectic GeometryMathematicsLemma (mathematics)Transitive relationRecurrence relationgeneric properties010102 general mathematicsMathematical analysissmooth dynamical systemsGeneral Medicine16. Peace & justicechain recurrence010101 applied mathematicsconnecting lemmaDiffeomorphism
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Some Inclusion Theorems for Orlicz and Musielak-Orlicz Type Spaces

1995

where K is a homogeneous kernel and f belongs to some KSthe functional space. In these papers the estimates are taken with respect to the KSthe norm of the space. Recently in [2] we obtained analogous estimates for functions belonging to Orlicz or Musielak-Orlicz type spaces L ~, with respect to the canonical modular functional. These results enable us to say that, for example,

Pure mathematicsMusielak-Orlicz spacesApplied MathematicsNorm (mathematics)Mathematical analysisFunctional spaceBirnbaum–Orlicz spaceOrlicz spacesRiemann-Liouville fractional integralHomogeneous kernelOrlicz spaces; Musielak-Orlicz spaces; Riemann-Liouville fractional integral; homogeneous kernelshomogeneous kernelsMathematics
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