Max Planck Institute for Mathematics in the Sciences

Dirichlet domains for Anosov subgroups

Abstract We introduce a sufficient condition for a finitely generated subgroup Γ of a semisimple Lie group 𝐺 to admit finite-sided Dirichlet domains for polyhedral Finsler metrics on the symmetric space G / K G/K . The condition always implies the Θ-Anosov condition for some Θ, a...

Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators

We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak...

A simple characterization of Quillen adjunctions

Abstract We observe that an enriched right adjoint functor between enriched model categories which preserves acyclic fibrations and fibrant objects is quite generically a right Quillen functor.

Approximately optimal search on a higher-dimensional sliding puzzle

Abstract Higher-dimensional sliding puzzles are constructed on the vertices of a d -dimensional hypercube, where $$2^d-l$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>d</mml:mi> </mml:msup> <mml:mo>-</mml:mo> <mml:mi>...