scholarly journals Hyperbolic metrics on open subsets of Ptolemaic spaces with sharp parameter bounds

2020 ◽  
pp. 1
Author(s):  
Neil N. Katz
Keyword(s):  
Hyperbolic Metrics ◽  
Parameter Bounds

Estimation of parameter bounds from bounded-error data: a survey

1990 ◽  
Vol 32 (5-6) ◽  
pp. 449-468 ◽  
Author(s):  
Eric Walter ◽  
Hélène Piet-Lahanier
Keyword(s):  
Bounded Error ◽  
Parameter Bounds

scholarly journals Topological flows for hyperbolic groups

2020 ◽  
pp. 1-47
Author(s):  
RYOKICHI TANAKA
Keyword(s):  
Hausdorff Dimension ◽  
Radon Measure ◽  
Hyperbolic Group ◽  
Hyperbolic Metric ◽  
Hyperbolic Groups ◽  
Group Invariant ◽  
Hyperbolic Metrics ◽  
Measure Class

Abstract Weshow that for every non-elementary hyperbolic group the Bowen–Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of maximal Hausdorff dimension on the boundary square. Applications include a characterization of roughly similar hyperbolic metrics via mean distortion.

scholarly journals Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces

2017 ◽  
Vol 2019 (16) ◽  
pp. 5012-5065 ◽  
Author(s):  
Richard Melrose ◽  
Xuwen Zhu
Keyword(s):  
Moduli Spaces ◽  
Asymptotic Expansions ◽  
Conformal Factor ◽  
Complex Structures ◽  
Stable Range ◽  
Universal Curve ◽  
Boundary Behaviour ◽  
Hyperbolic Metrics ◽  
Push Forward ◽  
Complete Metrics

Abstract The Weil–Petersson and Takhtajan–Zograf metrics on the Riemann moduli spaces of complex structures for an $n$-fold punctured oriented surface of genus $g,$ in the stable range $g+2n>2,$ are shown here to have complete asymptotic expansions in terms of Fenchel–Nielsen coordinates at the exceptional divisors of the Knudsen–Deligne–Mumford compactification. This is accomplished by finding a full expansion for the hyperbolic metrics on the fibres of the universal curve as they approach the complete metrics on the nodal curves above the exceptional divisors and then using a push-forward theorem for conormal densities. This refines a two-term expansion due to Obitsu–Wolpert for the conformal factor relative to the model plumbing metric which in turn refined the bound obtained by Masur. A similar expansion for the Ricci metric is also obtained.

scholarly journals Conformal Compactification of Asymptotically Locally Hyperbolic Metrics

2010 ◽  
Vol 21 (4) ◽  
pp. 1085-1118 ◽  
Author(s):  
Eric Bahuaud ◽  
Romain Gicquaud
Keyword(s):  
Hyperbolic Metrics

scholarly journals Confidence intervals with a priori parameter bounds

2015 ◽  
Vol 46 (3) ◽  
pp. 347-365 ◽  
Author(s):  
A. V. Lokhov ◽  
F. V. Tkachov
Keyword(s):  
Confidence Intervals ◽  
A Priori ◽  
Parameter Bounds
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