6 citations · 9 across the 3 of their papers we have counts for
5 papers
Chromatic numbers for the hyperbolic plane and discrete analogs
Hugo Parlier, Camille Petit
We study colorings of the hyperbolic plane, analogously to the Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points using the minimum number of colors such…
Chromatic numbers of hyperbolic surfaces
Hugo Parlier, Camille Petit
This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the -chromatic number is the minimum number of colors needed to color the points of the space…
Wolfe's theorem for weakly differentiable cochains
Camille Petit, Kai Rajala, Stefan Wenger
A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension in with the space of flat -cochains, that is, the du…
Boundary behaviour of harmonic functions on hyperbolic manifolds
Camille Petit
Let be a complete simply connected manifold which is in addition Gromov hyperbolic, coercive and roughly starlike. For a given harmonic function on , a local Fatou Theorem a…
Harmonic functions on hyperbolic graphs
Camille Petit
We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-t…