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Relevant bibliographies by topics / Carathéodory metric

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Journal articles

Academic literature on the topic 'Carathéodory metric'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Carathéodory metric"

1

Fornæss, John Erik, and Lina Lee. "Kobayashi, Carathéodory and Sibony metric." Complex Variables and Elliptic Equations 54, no. 3-4 (2009): 293–301. http://dx.doi.org/10.1080/17476930902760450.

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2

Abate, Marco, and Jean-Pierre Vigué. "Isometries for the Carathéodory metric." Proceedings of the American Mathematical Society 136, no. 11 (2008): 3905–9. http://dx.doi.org/10.1090/s0002-9939-08-09391-x.

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3

Ge, Zhong. "Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians." Canadian Journal of Mathematics 45, no. 3 (1993): 537–53. http://dx.doi.org/10.4153/cjm-1993-028-6.

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AbstractWe study the asymptotic behavior of the Laplacian on functions when the underlying Riemannian metric is collapsed to a Carnot-Carathéodory metric. We obtain a uniform short time asymptotics for the trace of the heat kernel in the case when the limit Carnot-Carathéodory metric is almost Heisenberg, the limit of which is the result of Beal-Greiner-Stanton, and Stanton-Tartakoff.

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4

CONNELL, CHRIS, THANG NGUYEN, and RALF SPATZIER. "Carnot metrics, dynamics and local rigidity." Ergodic Theory and Dynamical Systems 42, no. 2 (2021): 614–64. http://dx.doi.org/10.1017/etds.2021.116.

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AbstractThis paper develops new techniques for studying smooth dynamical systems in the presence of a Carnot–Carathéodory metric. Principally, we employ the theory of Margulis and Mostow, Métivier, Mitchell, and Pansu on tangent cones to establish resonances between Lyapunov exponents. We apply these results in three different settings. First, we explore rigidity properties of smooth dominated splittings for Anosov diffeomorphisms and flows via associated smooth Carnot–Carathéodory metrics. Second, we obtain local rigidity properties of higher hyperbolic rank metrics in a neighborhood of a loc

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5

Fu, Siqi. "Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains." Canadian Mathematical Bulletin 38, no. 2 (1995): 196–206. http://dx.doi.org/10.4153/cmb-1995-028-9.

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AbstractIn this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper can be stated as following:Main Theorem. Let Ω be a strictly pseudoconvex domain with C∞ smooth boundary. Let FΩ(z,X) be either the Carathéodory or the Kobayashi metric of Ω. Let δ(z) be the signed distance from z to ∂Ω with δ(z) < 0 for z ∊ Ω and δ(z) ≥ 0 for z ∉ Ω. Then there exist a neighborhood U of ∂Ω, a constant C > 0, and a continuous function C(z,X):(U ∩ Ω) × ℂn -> ℝ such that and|C(z

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6

Krushkal, Samuel. "On the Carathéodory metric of universal Teichmüller space." Ukrainian Mathematical Bulletin 19, no. 1 (2022): 75–87. http://dx.doi.org/10.37069/1810-3200-2029-19-1-5.

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In contrast to finite dimensional Teichmuller spaces, all non-expanding invariant metrics on the universal Teichmuller space coincide. This important fact found various applications. We give its new, simplified proof based on some deep features of the Grunsky operator, which intrinsically relate to the universal Teichmuller space. This approach also yields a quantitative answer to Ahlfors' question.

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7

Krushkal, Samuel L. "On the Carathéodory metric of universal Teichmüller space." Journal of Mathematical Sciences 262, no. 2 (2022): 184–93. http://dx.doi.org/10.1007/s10958-022-05809-9.

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8

Selivanova, Svetlana. "Metric Geometry of Nonregular Weighted Carnot–Carathéodory Spaces." Journal of Dynamical and Control Systems 20, no. 1 (2013): 123–48. http://dx.doi.org/10.1007/s10883-013-9206-3.

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9

Nikolov, N. "Continuity and boundary behavior of the Carathéodory metric." Mathematical Notes 67, no. 2 (2000): 183–91. http://dx.doi.org/10.1007/bf02686245.

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10

Świątkowski, Jacek. "Compact 3-manifolds with a flat Carnot-Carathéodory metric." Colloquium Mathematicum 63, no. 1 (1992): 89–105. http://dx.doi.org/10.4064/cm-63-1-89-105.

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