Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Danciger, Jeffrey"'
We prove a general combination theorem for discrete subgroups of $\mathrm{PGL}(n,\mathbb{R})$ preserving properly convex open subsets in the projective space $\mathbb{P}(\mathbb{R}^n)$, in the spirit of Klein and Maskit. We use it in particular to pr
Externí odkaz:
http://arxiv.org/abs/2407.09439
We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such representa
Externí odkaz:
http://arxiv.org/abs/2102.02757
In the early 1980's Margulis startled the world by showing the existence of proper affine actions of free groups on 3-space, answering a provocative and suggestive question Milnor posed in 1977. In this paper we discuss the historical background moti
Externí odkaz:
http://arxiv.org/abs/2002.09520
We study a notion of "width" for Jordan curves in $\mathbb{CP}^1$, paying special attention to the class of quasicircles. The width of a Jordan curve is defined in terms of the geometry of its convex hull in hyperbolic three-space. A similar invarian
Externí odkaz:
http://arxiv.org/abs/1908.09175
Publikováno v:
Geom. Topol. 25 (2021) 2827-2911
Celebrated work of Alexandrov and Pogorelov determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space. As a step toward a generalization for unbounded convex subsets, we consider c
Externí odkaz:
http://arxiv.org/abs/1902.04027
Autor:
Danciger, Jeffrey, Zhang, Tengren
Properly discontinuous actions of a surface group by affine automorphisms of $\mathbb R^d$ were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear part of an affine surface group action is in the Hitchin component, then
Externí odkaz:
http://arxiv.org/abs/1812.03930
Publikováno v:
Duke Math. J. 169, no. 12 (2020), 2231-2280
For any right-angled Coxeter group $\Gamma$ on $k$ generators, we construct proper actions of $\Gamma$ on $\mathrm{O}(p,q+1)$ by right and left multiplication, and on the Lie algebra $\mathfrak{o}(p,q+1)$ by affine transformations, for some $p,q\in\m
Externí odkaz:
http://arxiv.org/abs/1804.03132
We study a notion of convex cocompactness for discrete subgroups of the projective general linear group acting (not necessarily irreducibly) on real projective space, and give various characterizations. A convex cocompact group in this sense need not
Externí odkaz:
http://arxiv.org/abs/1704.08711
Anosov representations of word hyperbolic groups into higher-rank semisimple Lie groups are representations with finite kernel and discrete image that have strong analogies with convex cocompact representations into rank-one Lie groups. However, the
Externí odkaz:
http://arxiv.org/abs/1701.09136
A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean balls in
Externí odkaz:
http://arxiv.org/abs/1602.03865