7 citations · 18 across the 12 of their papers we have counts for
14 papers
The triangular metric on projective surfaces
León Carvajales, Xian Dai, Beatrice Pozzetti +1
In \cite{ThurstonStretch} Thurston introduced stretch paths and stretch maps between hyperbolic surfaces. In this paper we extend similar constructions to the space of convex real…
Finsler metrics on -translation structures on surfaces
Beatrice Pozzetti, Jiajun Shi
We define compatible Finsler distances on -translation surfaces, we study their geodesics, and construct a Liouville current for each such metric, that is a geodesic current t…
Positivity, cross-ratios and the Collar Lemma
Jonas Beyrer, Olivier Guichard, François Labourie +2
We prove that -positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are pos…
Geometry of hyperconvex representations of surface groups
James Farre, Beatrice Pozzetti, Gabriele Viaggi
We study the geometry of hyperconvex representations of surface groups in and their deformation spaces: We produce a natural holomorphic extension of the…
Topological and geometric restrictions on hyperconvex representations
James Farre, Beatrice Pozzetti, Gabriele Viaggi
We study the geometry of hyperconvex representations of hyperbolic groups in and establish two structural results: a group admitting a hyperconvex represe…
Metric properties of boundary maps, Hilbert entropy and non-differentiability
Beatrice Pozzetti, Andrés Sambarino
We interpret the Hilbert entropy of a convex projective structure on a closed higher-genus surface as the Hausdorff dimension of the non-differentiability points of the limit set i…
Thurston's asymmetric metrics for Anosov representations
León Carvajales, Xian Dai, Beatrice Pozzetti +1
We provide a good dynamical framework allowing to generalize Thurston's asymmetric metric and the associated Finsler norm from Teichmüller space to large classes of Anosov represen…
Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices
Federico López, Beatrice Pozzetti, Steve Trettel +2
We propose the use of the vector-valued distance to compute distances and extract geometric information from the manifold of symmetric positive definite matrices (SPD), and develop…
Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach
Federico López, Beatrice Pozzetti, Steve Trettel +2
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the sys…
Positive surface group representations in PO(p,q)
Jonas Beyrer, Beatrice Pozzetti
We show that -positive Anosov representations of a surface group satisfy root versus weight collar lemmas for all the Anosov roots, and are positively…
Degenerations of k-positive surface group representations
Jonas Beyrer, Beatrice Pozzetti
We introduce \emph{k-positive representations}, a large class of --Anosov surface group representations into PGL(E) that share many features with Hitchin representa…
Hermitian Symmetric Spaces for Graph Embeddings
Federico López, Beatrice Pozzetti, Steve Trettel +1
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the…
Hessian of Hausdorff dimension on purely imaginary directions
Martin Bridgeman, Beatrice Pozzetti, Andrés Sambarino +1
We extend classical results of Bridgeman-Taylor and McMullen on the Hessian of the Hausdorff dimension on quasi-Fuchsian space to the class of (1,1,2)-hyperconvex representations,…
A collar lemma for partially hyperconvex surface group representations
Jonas Beyrer, Beatrice Pozzetti
We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into $\SL(n,\R)$ that satisfy partial hyperconvexity properties inspired from Labouri…