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Entropy, minimal surfaces and negatively curved manifolds

Abstract (Expand)

Taubes [Minimal surfaces in germs of hyperbolic 3-manifolds. Proceedings of the Casson Fest, Geom. Topol. Monogr. 7 (2004), 69–100 (electronic)] introduced the space of minimal hyperbolic germs with … elements consisting of the first and second fundamental form of an equivariant immersed minimal disk in hyperbolic 3-space. Herein, we initiate a further study of this space by studying the behavior of a dynamically defined function which records the entropy of the geodesic flow on the associated Riemannian surface. We provide a useful estimate on this function which, in particular, yields a new proof of Bowen’s theorem on the rigidity of the Hausdorff dimension of the limit set of quasi-Fuchsian groups. These follow from new lower bounds on the Hausdorff dimension of the limit set which allow us to give a quantitative version of Bowen’s rigidity theorem. To demonstrate the strength of the techniques, these results are generalized to convex-cocompact surface groups acting on n-dimensional \mathrmCAT(-1) Riemannian manifolds.

Author: ANDREW SANDERS

Date Published: 1st Feb 2018

Publication Type: Journal

Convective–reactive nucleosynthesis of K, Sc, Cl and p-process isotopes in O–C shell mergers

Abstract

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Authors: C Ritter, R Andrassy, B Côté, F Herwig, P R Woodward, M Pignatari, S Jones

Date Published: 1st Feb 2018

Publication Type: Journal

SABIO-RK: an updated resource for manually curated biochemical reaction kinetics

Abstract

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Authors: Ulrike Wittig, Maja Rey, Andreas Weidemann, Renate Kania, Wolfgang Müller

Date Published: 4th Jan 2018

Publication Type: Journal

Photometric redshift estimation via deep learning. Generalized and pre-classification-less, image based, fully probabilistic redshifts

Abstract

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Authors: A. D’Isanto, K. L. Polsterer

Date Published: 2018

Publication Type: Journal

OpenGL® API-Based Analysis of Large Datasets in a Cloud Environment

Abstract

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Authors: Wolfgang Mexner, Matthias Bonn, Andreas Kopmann, Viktor Mauch, Doris Ressmann, Suren A. Chilingaryan, Nicholas Tan Jerome, Thomas Van De Kamp, Vincent Heuveline, Philipp Lösel, et al.

Date Published: 2018

Publication Type: Journal

Return of the features - Efficient feature selection and interpretation for photometric redshifts

Abstract

Not specified

Authors: A. D\’Isanto, S. Cavuoti, F. Gieseke, K. L. Polsterer

Date Published: 2018

Publication Type: Journal

Design and Implementation of I/O-Efficient Taxa Quartets Counting in the Context of Phylogenetic Analysis

Abstract

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Author: Linda Rülicke

Date Published: 2018

Publication Type: Master's Thesis

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