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81 Publications visible to you, out of a total of 81
The pressure metric on the Margulis multiverse

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This paper defines the pressure metric on the Moduli space of Margulis spacetimes without cusps and shows that it is positive definite on the constant entropy sections. It also demonstrates an identity … regarding the variation of the cross-ratios.

Author: Sourav Ghosh

Date Published: 1st Apr 2018

Publication Type: Journal

Convex projective generalized Dehn filling

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For d = 4,5,6, we exhibit the first examples of complete finite volume hyperbolic d-manifolds M with cusps such that infinitely many d-orbifolds M_m obtained from M by generalized Dehn filling admit … properly convex real projective structures. The orbifold fundamental groups of M_m are Gromov-hyperbolic relative to a collection of subgroups virtually isomorphic to \mathbbZ^d-2, hence the images of the developing maps of the projective structures on M_m are new examples of divisible properly convex domains of the projective d-space which are not strictly convex, in contrast to the previous examples of Benoist.

Authors: Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis

Date Published: 30th Mar 2018

Publication Type: Journal

Deforming convex real projective structures

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Let S be a closed, connected, orientable surface of genus at least 2, and let C(S) denote the deformation space of convex real projective structures S. In this article, we introduce two new flows on … C(S), which we call the internal bulging flow and the eruption flow. These are geometrically defined flows associated to each pair of pants in a pants decomposition on S that deform the internal parameters. We show that the eruption flows, together with the generalized twist flows about the pants curves, give rise to a half-dimensional family of commuting flows on C(S).

Authors: Anna Wienhard, Tengren Zhang

Date Published: 1st Feb 2018

Publication Type: Journal

Mapping class group orbits of curves with self-intersections

Abstract

Not specified

Authors: Patricia Cahn, Federica Fanoni, Bram Petri

Date Published: 1st Feb 2018

Publication Type: Journal

Entropy, minimal surfaces and negatively curved manifolds

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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

Toric Varieties vs. Horofunction Compactifications of Polyhedral Norms

Abstract

Not specified

Authors: Lizhen Ji, Anna-Sofie Schilling

Date Published: 2018

Publication Type: Journal

Graphs of curves on infinite-type surfaces with mapping class group actions

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We study when the mapping class group of an infinite-type surface S admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on S. We introduce a topological … invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us to conclude that, as non-locally compact topological groups, many big mapping class groups have nontrivial coarse geometry in the sense of Rosendal.

Authors: Matthew Gentry Durham, Federica Fanoni, Nicholas G. Vlamis

Date Published: 2018

Publication Type: Book

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