8 papers
Ideal Poisson--Voronoi tessellations for Finsler metrics on symmetric spaces
Colin Davalo, J. Maxwell Riestenberg, Anna Wienhard
Ideal Poisson--Voronoi tessellations are random tessellations that arise as limits of Voronoi diagrams for Poisson point processes as their intensity tends to zero. For the Riemann…
Harmonic maps to Hadamard spaces and a universal higher Teichmüller space
J. Maxwell Riestenberg, Peter Smillie
We give a sufficient criterion, which we call stability, for a coarse Lipschitz map from a complete manifold with Ricci curvature bounded below to a proper Hadamard space $…
Transverse Spheres in Flag Manifolds
Parker Evans, J. Maxwell Riestenberg
For some partial flag manifolds of semisimple real Lie groups, including many full flag manifolds, transverse circles are known to be locally maximally transverse. We complete the…
Concave Foliated Flag Structures and the Hitchin Component
Alexander Nolte, J. Maxwell Riestenberg
We give a geometric characterization of flag geometries associated to Hitchin representations in . Our characterization is based on distinguished invariant…
Dirichlet domains for Anosov subgroups
Colin Davalo, J. Maxwell Riestenberg
We introduce a sufficient condition for a finitely generated subgroup of a semisimple Lie group to admit finite-sided Dirichlet domains for polyhedral Finsler metrics on th…
Normed Spaces for Graph Embedding
Diaaeldin Taha, Wei Zhao, J. Maxwell Riestenberg +1
Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimens…
Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices
Wei Zhao, Federico Lopez, J. Maxwell Riestenberg +3
Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data…
A quantified local-to-global principle for Morse quasigeodesics
J. Maxwell Riestenberg
In arXiv:1403.7671, Kapovich, Leeb and Porti gave several new characterizations of Anosov representations , including one where geodesics in the word hyperbolic group m…