Results 271 to 280 of about 7,754 (304)

Comparison Between a Gromov Hyperbolic Metric and the Hyperbolic Metric

Computational Methods and Function Theory, 2018
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Xiaohui Zhang
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Deforming an є-close-to-hyperbolic metric to a hyperbolic metric [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2018
We show how to deform a metric of the form g = gr + dr2 to a metric = Hr + dr2, which is a hyperbolic metric for r less than some fixed λ, and coincides with g for r large. Here by hyperbolic metric we mean a metric of constant sectional curvature equal to -1.
Pedro Ontaneda
openaire   +2 more sources

Inequalities for a new hyperbolic type metric [PDF]

Complex Analysis and Its Synergies
We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequalities with the hyperbolic metric and the triangular ratio metric.
Oona Rainio, Rainio Oona
exaly   +6 more sources

Unsupervised Hyperbolic Metric Learning

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021
Learning feature embedding directly from images without any human supervision is a very challenging and essential task in the field of computer vision and machine learning. Following the paradigm in supervised manner, most existing unsupervised metric learning approaches mainly focus on binary similarity in Euclidean space.
Jiexi Yan, Lei Luo 0001, Cheng Deng 0002, Heng Huang 0001   +3 more
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Quotients of Hyperbolic Metrics

Computational Methods and Function Theory, 2017
The author estimates the quotient of the hyperbolic metrics of two hyperbolic domains on the Riemann sphere, one being a proper subset of the other. The bounds for the quotients are useful in complex dynamics. The purpose of this paper is to show their importance for the theory of hyperbolic metric.
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Hyperbolic Extensions and Metrics ε-Close to Hyperbolic

Indiana University Mathematics Journal, 2017
The paper "Pinched Smooth Hyperbolization" [arXiv:1110.6374] has been divided in parts.
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THE HILBERT METRIC AND GROMOV HYPERBOLICITY

2002
Given a convex domain \(D\) in the Euclidean space, for any pair of points \(x\) and \(y\) in \(D\) let us denote by \(x^\prime\) and \(y^\prime\) the intersections of the line through \(x\) and \(y\) with the boundary of \(D\) closest to \(x\) and \(y\). The logarithm of the crossratio of these four points defines the Hilbert metric on \(D\): \(h(x,y)
Karlsson, Anders, Noskov, Guennadi A.
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Hyperbolic Type Metrics

2020
In Chaps. 4 and 5 we studied the quasihyperbolic metric kD ( 5.2) and the distance ratio metric jD ( 4.27). These two metrics are generalizations of the hyperbolic metric (Chap. 4) and in this chapter we introduce other such generalizations.
Parisa Hariri, Riku Klén, Matti Vuorinen   +2 more
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