Search results for "Map"

showing 10 items of 3484 documents

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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Disjointness of Lattice Elements

1992

We examine the relations between various disjointness properties in lattices with least elements, and in special lattices like section semicomplemented lattices and section complemented lattices.

Pure mathematicsHigh Energy Physics::LatticeGeneral MathematicsLattice (order)Map of latticesMathematicsMathematische Nachrichten
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On the structure of the set of solutions of nonlinear equations

1971

Let T be a mapping from a subset of a Banach space X into a Banach space Y. The present paper investigates the nature of the set of solutions of the equation T(x) = y for a given y E Y, i.e. when T-l(y) # 0 ? What are the topological properties of T-l(y)? A prototype for an answer to these questions is given by Peano existence theorem on the connectedness of the set of solutions of an ordinary differential equation in the real case. In its general setting, this problem was first attacked by Aronszajn [l] and Stampacchia [l 11; recently, by Browder-Gupta [5], Vidossich [12] and, above all, Browder [3, Sec. 51 who gives several interesting results in an excellent treatment. Customary, the str…

Pure mathematicsIndependent equationApplied MathematicsProper mapOrdinary differential equationBanach spaceExistence theoremOpen and closed mapsAnalysisDomain (mathematical analysis)MathematicsPeano existence theoremJournal of Mathematical Analysis and Applications
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From metric spaces to partial metric spaces

2013

Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced. MSC:47H10, 54H25.

Pure mathematicsInjective metric spaceApplied MathematicsMathematical analysismetric spacepartial metric spaceEquivalence of metricsIntrinsic metricConvex metric spaceMetric spaceUniform continuityfixed pointFréchet spaceSettore MAT/05 - Analisi MatematicaMetric mapGeometry and TopologyMathematicsFixed Point Theory and Applications
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Best proximity point results for modified α-proximal C-contraction mappings

2014

First we introduce new concepts of contraction mappings, then we establish certain best proximity point theorems for such kind of mappings in metric spaces. Finally, as consequences of these results, we deduce best proximity point theorems in metric spaces endowed with a graph and in partially ordered metric spaces. Moreover, we present an example and some fixed point results to illustrate the usability of the obtained theorems. MSC:46N40, 46T99, 47H10, 54H25.

Pure mathematicsInjective metric spaceApplied Mathematicsmetric spacebest proximity pointFixed pointTopologyConvex metric spaceIntrinsic metricLeast fixed pointMetric spacefixed pointSettore MAT/05 - Analisi MatematicaMetric mapGeometry and TopologyCoincidence pointMathematicsFixed Point Theory and Applications
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Completely positive invariant conjugate-bilinear maps on partial *-algebras

2007

The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of commutative, locally convex quasi*-algebras are also discussed.

Pure mathematicsIntegrable systemApplied MathematicsRegular polygonFOS: Physical sciencesBilinear interpolationMathematical Physics (math-ph)Completely positive mapSettore MAT/05 - Analisi MatematicaPartial O*-algebrasPartial *-algebraInvariant (mathematics)Commutative propertySettore MAT/07 - Fisica MatematicaAnalysisMathematical PhysicsConjugateMathematics
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Bonnesenʼs inequality for John domains in Rn

2012

Abstract We prove sharp quantitative isoperimetric inequalities for John domains in R n . We show that the Bonnesen-style inequalities hold true in R n under the John domain assumption which rules out cusps. Our main tool is a proof of the isoperimetric inequality for symmetric domains which gives an explicit estimate for the isoperimetric deficit. We use the sharp quantitative inequalities proved in Fusco et al. (2008) [7] and Fuglede (1989) [4] to reduce our problem to symmetric domains.

Pure mathematicsJohn domainInequalitymedia_common.quotation_subjectMathematical analysisIsoperimetric dimensionQuasiconformal mapDomain (mathematical analysis)Quantitative isoperimetric inequalityMathematics::Metric GeometryIsoperimetric inequalityAnalysismedia_commonMathematicsJournal of Functional Analysis
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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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Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces

2003

Abstract We use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces. The metric spaces under consideration are those that are endowed with a doubling measure supporting a (1,2)-Poincare inequality and in addition supporting a corresponding Sobolev–Poincare-type inequality for the modification of the measure obtained via the heat kernel. Examples are given to illustrate the necessity of our assumptions on these spaces. We also provide an example to show that in the general setting the best possible regularity for the Cheeger-harmonic functions is Lipschitz continuity.

Pure mathematicsMathematical analysisLipschitz continuityModulus of continuityCheeger-harmonicConvex metric spaceUniform continuityMetric spaceLipschitz domainPoincaré inequalityheat kerneldoubling measureMetric mapLipschitz regularitylogarithmic Sobolev inequalityMetric differentialhypercontractivityAnalysisNewtonian spaceMathematicsJournal of Functional Analysis
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Supermanifolds, Symplectic Geometry and Curvature

2016

We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.

Pure mathematicsMathematical analysisSymplectic representationGeneral Relativity and Quantum CosmologyHigh Energy Physics::TheorySymplectic vector spaceMathematics::Differential GeometrySymplectomorphismMathematics::Symplectic GeometryMoment mapGeometry and topologyScalar curvatureSymplectic geometrySymplectic manifoldMathematics
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