4 citations · 8 across the 10 of their papers we have counts for
11 papers
Holmes-Thompson area of inscribed polygons and convex projective structures
Xenia Flamm, Giuseppe Martone
Positive tuples of complete flags in define two convex polygons in , one inscribed in the other. We are interested in relating the Holmes-Thompson are…
Topology of the space of -pleated surfaces
Sara Maloni, Giuseppe Martone, Filippo Mazzoli +1
Given a maximal geodesic lamination on a closed oriented surface of genus , the space of -pleated surfaces with pleating locus is an open subset of $\mathrm{Hom}(…
Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations
Lien-Yung Kao, Giuseppe Martone
We introduce a correlation number for two strictly positive, locally Hölder continuous, independent potentials with strong entropy gaps at infinity on a topologically mixing counta…
-pleated surfaces and their shear-bend coordinates
Sara Maloni, Giuseppe Martone, Filippo Mazzoli +1
In this article, we single out representations of surface groups into which generalize the well-studied family of pleated surfaces into $\mathsf{PSL}_2…
Pressure metrics for cusped Hitchin components
Harrison Bray, Richard Canary, Lien-Yung Kao +1
We study the cusped Hitchin component consisting of (conjugacy classes of) cusped Hitchin representations of a torsion-free geometrically finite Fuchsian group into PSL(d,R). We pr…
A closed ball compactification of a maximal component via cores of trees
Giuseppe Martone, Charles Ouyang, Andrea Tamburelli
We show that, in the character variety of surface group representations into the Lie group , the compactification of t…
Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations
Harrison Bray, Richard Canary, Lien-Yung Kao +1
We show that if an eventually positive, non-arithmetic, locally Hölder continuous potential for a topologically mixing countable Markov shift with (BIP) has an entropy gap at infin…
Correlation of the renormalized Hilbert length for convex projective surfaces
Xian Dai, Giuseppe Martone
In this paper we focus on dynamical properties of (real) convex projective surfaces. Our main theorem provides an asymptotic formula for the number of free homotopy classes with ro…
Sequences of Hitchin representations of Tree-type
Giuseppe Martone
The Hitchin component is a connected component of the character variety of reductive group homomorphisms from the fundamental group of a closed surface S of genus greater than 1 to…
Positive configurations of flags in a building and limits of positive representations
Giuseppe Martone
Parreau compactified the Hitchin component of a closed surface of negative Euler characteristic in such a way that a boundary point corresponds to the projectivized length spec…
Positively ratioed representations
Giuseppe Martone, Tengren Zhang
Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundame…