publications | Antoine Clais

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

Antoine Clais

Comptes Rendus Mathematique, 2017

Bib PDF

@article{CLAIS2017819,
  title = {Conformal dimension on boundary of right-angled hyperbolic buildings},
  journal = {Comptes Rendus Mathematique},
  volume = {355},
  number = {7},
  pages = {819-823},
  year = {2017},
  issn = {1631-073X},
  doi = {https://doi.org/10.1016/j.crma.2017.06.006},
  url = {https://www.sciencedirect.com/science/article/pii/S1631073X17301747},
  author = {Clais, Antoine}
}

2016

Transitive parallelism of residues in buildings

Antoine Clais

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2016

Bib PDF

@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},
}

Antoine Clais

Analysis and Geometry in Metric Spaces, 2016

Bib PDF

@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

Antoine Clais

Séminaire TSG (Grenoble), 2015

Bib PDF

@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

Antoine Clais

Dec 2014

Bib PDF

@phdthesis{clais:tel-01110542,
  title = {Right-angled buildings and combinatorial modulus on the boundary},
  author = {Clais, Antoine},
  url = {https://hal.science/tel-01110542},
  school = {Universit{\'e} Lille 1},
  year = {2014},
  month = dec,
  keywords = {Hyperbolic spaces ; Combinatorial Loewner property ; Buildings ; Boundaries ; Combinatorial modulus ; Espaces hyperboliques ; Immeubles ; Bord ; Propri{\'e}t{\'e} de Loewner combinatoire ; modules combinatoires},
  type = {Theses},
  hal_id = {tel-01110542},
  hal_version = {v1}
}