My work is related to the following topics: hyperbolic groups, Coxeter groups, buildings, cube complexes, quasi-conformal analysis on boundaries, combinatorial modulus of curves, conformal dimension and combinatorial Loewner property.
More precisly, I study the quasi-conformal structures on boundaries of hyperbolic groups. Following ideas of Mostow, Gromov and Pansu, these properties can imply rigidity phenomenon in the group. In particular, I work on boundaries of right-angled hyperbolic buildings of dimension 3 and 4 whose boundaries that are highly suspected to be QI-rigid.
These researches have excited my curiosity in the theories of buildings, hyperbolic geometry and hyperbolic groups and generalizations.
2017
Conformal dimension on boundary of right-angled hyperbolic buildings
@article{10.36045/bbms/1480993592,author={Clais, Antoine},title={Transitive parallelism of residues in buildings},volume={23},journal={Bulletin of the Belgian Mathematical Society - Simon Stevin},number={4},publisher={The Belgian Mathematical Society},pages={625 -- 640},keywords={buildings, Coxeter groups, parabolic subgroups, parallel residues},year={2016},doi={10.36045/bbms/1480993592},url={https://doi.org/10.36045/bbms/1480993592},}
@article{Clais+2016,url={https://doi.org/10.1515/agms-2016-0001},title={},author={Clais, Antoine},pages={000010151520160001},volume={4},number={1},journal={Analysis and Geometry in Metric Spaces},doi={doi:10.1515/agms-2016-0001},year={2016},lastchecked={2024-06-20},}
2015
Propriétés combinatoires du bord d’un groupe hyperbolique
@article{ClaisTSG,title={Propriétés combinatoires du bord d'un groupe hyperbolique},author={Clais, Antoine},journal={Séminaire TSG (Grenoble)},volume={32},pages={73--96},year={2015},url={https://proceedings.centre-mersenne.org/item/10.5802/tsg.304.pdf},}
2014
Right-angled buildings and combinatorial modulus on the boundary