Relevant bibliographies by topics / Sub-Finsler metric

Academic literature on the topic 'Sub-Finsler metric'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Sub-Finsler metric"

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Alabdulsada, Layth M., and László Kozma. "On the connections of sub-Finslerian geometry." International Journal of Geometric Methods in Modern Physics 16, supp02 (November 2019): 1941006. http://dx.doi.org/10.1142/s0219887819410068.

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A sub-Finslerian manifold is, roughly speaking, a manifold endowed with a Finsler type metric which is defined on a [Formula: see text]-dimensional smooth distribution only, not on the whole tangent manifold. Our purpose is to construct a generalized nonlinear connection for a sub-Finslerian manifold, called [Formula: see text]-connection by the Legendre transformation which characterizes normal extremals of a sub-Finsler structure as geodesics of this connection. We also wish to investigate some of its properties like normal, adapted, partial and metrical.
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REZAEI, BAHMAN, and MEHDI RAFIE-RAD. "ON THE PROJECTIVE ALGEBRA OF SOME (α, β)-METRICS OF ISOTROPIC S-CURVATURE." International Journal of Geometric Methods in Modern Physics 10, no. 10 (October 8, 2013): 1350048. http://dx.doi.org/10.1142/s0219887813500485.

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In this paper, we study projective algebra, p(M, F), of special (α, β)-metrics. The projective algebra of a Finsler space is a finite-dimensional Lie algebra with respect to the usual Lie bracket. We characterize p(M, F) of Matsumoto and square metrics of isotropic S-curvature of dimension n ≥ 3 as a certain Lie sub-algebra of the Killing algebra k(M, α). We also show that F has a maximum projective symmetry if and only if F either is a Riemannian metric of constant sectional curvature or locally Minkowskian.
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Berestovskii, V. N., and I. A. Zubareva. "Extremals of a Left-Invariant Sub-Finsler Metric on the Engel Group." Siberian Mathematical Journal 61, no. 4 (July 2020): 575–88. http://dx.doi.org/10.1134/s0037446620040023.

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Alfaro, Matthieu, Harald Garcke, Danielle Hilhorst, Hiroshi Matano, and Reiner Schätzle. "Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen–Cahn equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 4 (August 2010): 673–706. http://dx.doi.org/10.1017/s0308210508000541.

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We consider the spatially inhomogeneous and anisotropic reaction–diffusion equation ut = m(x)−1 div[m(x)ap(x,∇u)] + ε−2f(u), involving a small parameter ε > 0 and a bistable nonlinear term whose stable equilibria are 0 and 1. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and perform an analysis of both the generation and the motion of interfaces. More precisely, we show that, within the time-scale of order ε2|ln ε|, the unique weak solution uε develops a steep transition layer that separates the regions {uε ≈ 0} and {uε | 1}. Then, on a much slower time-scale, the layer starts to propagate. Consequently, as ε → 0, the solution uε converges almost everywhere (a.e.) to 0 in Ω−t and 1 in Ω+t , where Ω−t and Ω+t are sub-domains of Ω separated by an interface Гt, whose motion is driven by its anisotropic mean curvature. We also prove that the thickness of the transition layer is of order ε.
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Fisher, Nate, and Sebastiano Nicolussi Golo. "Sub-Finsler Horofunction Boundaries of the Heisenberg Group." Analysis and Geometry in Metric Spaces 9, no. 1 (January 1, 2021): 19–52. http://dx.doi.org/10.1515/agms-2020-0121.

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Abstract We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those that arise as asymptotic cones of word metrics, on the Heisenberg group. We develop theory for the more general case of horofunction boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives of the distance function.
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RAFIE-RAD, M. "SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1250034. http://dx.doi.org/10.1142/s021988781250034x.

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The collection of all projective vector fields on a Finsler space (M, F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most [Formula: see text]. Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.
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Le Donne, Enrico, Danka Lučić, and Enrico Pasqualetto. "Universal Infinitesimal Hilbertianity of Sub-Riemannian Manifolds." Potential Analysis, April 11, 2022. http://dx.doi.org/10.1007/s11118-021-09971-8.

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AbstractWe prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.
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Essebei, Fares, and Enrico Pasqualetto. "Variational problems concerning sub-Finsler metrics in Carnot groups." ESAIM: Control, Optimisation and Calculus of Variations, January 13, 2023. http://dx.doi.org/10.1051/cocv/2023006.

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This paper is devoted to the study of geodesic distances defined on a subdomain of a given Carnot group, which are bounded both from above and from below by fixed multiples of the Carnot–Carath´eodory distance. We show that the uniform convergence (on compact sets) of these distances can be equivalently characterized in terms of Γ-convergence of several kinds of variational problems. Moreover, we investigate the relation between the class of intrinsic distances, their metric derivatives and the sub-Finsler convex metrics defined on the horizontal bundle.
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Dissertations / Theses on the topic "Sub-Finsler metric"

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Essebei, Fares. "Variational problems for sub–Finsler metrics in Carnot groups and Integral Functionals depending on vector fields." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/345679.

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The first aim of this PhD Thesis is devoted to the study of geodesic distances defined on a subdomain of a Carnot group, which are bounded both from above and from below by fixed multiples of the Carnot–Carathéodory distance. Then one shows that the uniform convergence, on compact sets, of these distances can be equivalently characterized in terms of Gamma-convergence of several kinds of variational problems. Moreover, it investigates the relation between the class of intrinsic distances, their metric derivatives and the sub-Finsler convex metrics defined on the horizontal bundle. The second purpose is to obtain the integral representation of some classes of local functionals, depending on a family of vector fields, that satisfy a weak structure assumption. These functionals are defined on degenerate Sobolev spaces and they are assumed to be not translations-invariant. Then one proves some Gamma-compactness results with respect to both the strong topology of L^p and the strong topology of degenerate Sobolev spaces.
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