Search results for "Submanifold"

showing 3 items of 23 documents

A new rotational integral formula for intrinsic volumes in space forms

2010

A new rotational version of Crofton's formula is derived for the intrinsic volumes of a domain Y in a space form. More precisely, a functional is defined on the intersection between Y and a totally geodesic submanifold (plane) through a fixed point, such that the rotational average of this functional is equal to the intrinsic volumes of Y. Particular cases of interest in stereology are considered for the Euclidean case. © 2009 Elsevier Inc. All rights reserved.

TransversalityPlane (geometry)Space formApplied MathematicsStereologyMathematical analysisTransversalitySpace formFixed pointSubmanifoldSpace (mathematics)Integral geometryIntersectionMathematics::Metric GeometrySupport setIntegral geometryIntrinsic volumeRotational integralMathematics
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Minimum Time Control of the Restricted Three-Body Problem

2012

The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Surface (mathematics)0209 industrial biotechnologyControl and OptimizationApplied MathematicsHomotopy010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyThree-body problemOptimal controlSubmanifold01 natural sciencesControllability020901 industrial engineering & automationSimple (abstract algebra)Gravitational singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsMathematicsSIAM Journal on Control and Optimization
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Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces

2020

This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a -hypersurface without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of topological dimension 8, it has Hausdorff dimension 12 and so we use on it the Hausdorff measure . As a consequence, we show that any Lipschitz map defined on a subset of a Carnot group of Hausdorff dimension 12, with…

codimension-one rectifiabilitysmooth hypersurface1ryhmäteoriaIntrinsic Lipschitz graphIntrinsic rectifiable setsubmanifoldsdifferentiaaligeometriaIntrinsic Cintrinsic Lipschitz graphCarnot groupsSmooth hypersurfaceMathematics::Metric Geometryintrinsic rectifiable setmittateoriaCodimension-one rectifiabilityCarnot groups; Codimension-one rectifiability; Intrinsic C; 1; submanifolds; Intrinsic Lipschitz graph; Intrinsic rectifiable set; Smooth hypersurface
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