0000000000123750

AUTHOR

Pierre Pansu

showing 5 related works from this author

Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds

2012

Abstract We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Mathematics - Differential GeometryIsoperimetric dimensionRiemannian geometryTopology01 natural sciencessymbols.namesakeRicci-flat manifoldFOS: MathematicsDifferentiable functionMorse theory0101 mathematicsTopology (chemistry)Computer Science::DatabasesIsoperimetric inequalityMorse theoryMathematicsRiemann surface010102 general mathematicsGeneral Medicinecalibration53C20;49Q20;14P15;32B20010101 applied mathematicsDifferential Geometry (math.DG)Riemann surface[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]symbolsMathematics::Differential GeometryIsoperimetric inequality
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Bounded geometry, growth and topology

2010

We characterize functions which are growth types of Riemannian manifolds of bounded geometry.

Mathematics - Differential GeometryMathematics(all)bounded geometryGeneral MathematicsgrowthAbsolute geometryGeometryRiemannian geometry53C20Topology01 natural sciencesQuasi-isometriessymbols.namesakeGrowth types0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics::Symplectic GeometryGeometry and topologyMathematicsvolumeCurvature of Riemannian manifoldsApplied MathematicsComputer Science::Information Retrieval010102 general mathematicsMathematical analysisMathematics::Geometric Topologyfinite topological typeDifferential geometryDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Bounded functionsymbols010307 mathematical physicsMathematics::Differential GeometryConformal geometryGraphsSymplectic geometry
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Semianalyticity of isoperimetric profiles

2009

It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.

Mathematics - Differential Geometry0209 industrial biotechnologyRiemannian Geometry Real Analytic Geometry Geometric measure Theory Metric Geometry Geometric Analysis.Calibration (statistics)02 engineering and technologyAstrophysics::Cosmology and Extragalactic Astrophysics01 natural sciencessymbols.namesake020901 industrial engineering & automationFOS: MathematicsMathematics::Metric GeometryMorse theory0101 mathematicsMathematics::Symplectic GeometryIsoperimetric inequalityMorse theoryMathematicsRiemann surface010102 general mathematicsMathematical analysis53C20;49Q20;14P15;32B20Differential Geometry (math.DG)Computational Theory and Mathematics[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Riemann surfaceCalibrationsymbolsGeometry and TopologyMathematics::Differential GeometryIsoperimetric inequalityAnalysis
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Sur la r�gularit� de la fonction croissance d'une vari�t� riemannienne

1994

On etudie la differentiabilite de la fonction croissance d'une variete riemannienne complete. En general, elle a la meme regularite qu'une fonction concave: la derivee peut avoir des sauts pour lesquels on donne une formule. Dans le cas analytique reel, la fonction croissance est de classeC1. Un exemple montre qu'elle n'est pas necessairementC2. A titre d'application, nous construisons, pour toute variete ouverte paracompacteM et toute fonction croissantev de classeC1, une metrique continue de croissance egale av et une metrique de classeC∞ surM de croissance proche dev en topologieC1-fine.

Pure mathematicsDifferential geometryHyperbolic geometryGeometry and TopologyAlgebraic geometryMathematicsProjective geometryGeometriae Dedicata
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Sard property for the endpoint map on some Carnot groups

2016

In Carnot-Caratheodory or sub-Riemannian geometry, one of the major open problems is whether the conclusions of Sard's theorem holds for the endpoint map, a canonical map from an infinite-dimensional path space to the underlying finite-dimensional manifold. The set of critical values for the endpoint map is also known as abnormal set, being the set of endpoints of abnormal extremals leaving the base point. We prove that a strong version of Sard's property holds for all step-2 Carnot groups and several other classes of Lie groups endowed with left-invariant distributions. Namely, we prove that the abnormal set lies in a proper analytic subvariety. In doing so we examine several characterizat…

Mathematics - Differential Geometry0209 industrial biotechnologyPure mathematics53C17 22F50 22E25 14M17SubvarietyGroup Theory (math.GR)02 engineering and technologySard's property01 natural sciencesSet (abstract data type)020901 industrial engineering & automationAbnormal curves; Carnot groups; Endpoint map; Polarized groups; Sard's property; Sub-Riemannian geometry; Analysis; Mathematical PhysicsMathematics - Metric GeometryFOS: MathematicsPoint (geometry)Canonical mapAbnormal curves; Carnot groups Endpoint map Polarized groups Sard's property Sub-Riemannian geometry Analysis0101 mathematicsMathematics - Optimization and ControlMathematical PhysicsMathematicsApplied Mathematics010102 general mathematicsta111Polarized groupsCarnot groupLie groupEndpoint mapMetric Geometry (math.MG)Base (topology)ManifoldSub-Riemannian geometryDifferential Geometry (math.DG)Optimization and Control (math.OC)Carnot groupsAbnormal curvesMathematics - Group TheoryAnalysis
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