Geodesic
Affine isoperimetric inequalities on flag manifolds
Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 252-281

Voir la notice de l'article provenant de la source Cambridge

DOI

Building on work of Furstenberg and Tzkoni, we introduce $\mathbf {r}$-flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the Grassmannian can be considered as a special case). We establish affine and linear invariance properties and extend fundamental results to this new setting. In particular, we prove several affine isoperimetric inequalities from convex geometry and their approximate reverse forms. We also introduce functional forms of these quantities and establish corresponding inequalities.
DOI : 10.4153/S0008414X23000871
Mots-clés : Flag manifolds, (dual) affine quermassintegrals, (approximate reverse) isoperimetric inequalities, affine invariance 
Dann, Susanna; Paouris, Grigoris; Pivovarov, Peter. Affine isoperimetric inequalities on flag manifolds. Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 252-281. doi: 10.4153/S0008414X23000871
@article{10_4153_S0008414X23000871,
     author = {Dann, Susanna and Paouris, Grigoris and Pivovarov, Peter},
     title = {Affine isoperimetric inequalities on flag manifolds},
     journal = {Canadian journal of mathematics},
     pages = {252--281},
     year = {2025},
     volume = {77},
     number = {1},
     doi = {10.4153/S0008414X23000871},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000871/}
}
TY  - JOUR
AU  - Dann, Susanna
AU  - Paouris, Grigoris
AU  - Pivovarov, Peter
TI  - Affine isoperimetric inequalities on flag manifolds
JO  - Canadian journal of mathematics
PY  - 2025
SP  - 252
EP  - 281
VL  - 77
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000871/
DO  - 10.4153/S0008414X23000871
ID  - 10_4153_S0008414X23000871
ER  - 
%0 Journal Article
%A Dann, Susanna
%A Paouris, Grigoris
%A Pivovarov, Peter
%T Affine isoperimetric inequalities on flag manifolds
%J Canadian journal of mathematics
%D 2025
%P 252-281
%V 77
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000871/
%R 10.4153/S0008414X23000871
%F 10_4153_S0008414X23000871

Cité par Sources :