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arXiv · 1902.09076

Affine isoperimetric inequalities on flag manifolds

Susanna Dann·Grigoris Paouris·Peter Pivovarov
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Abstract

Building on work of Furstenberg and Tzkoni, we introduce ${\bf r}$-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.

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Susanna Dann, Grigoris Paouris, Peter Pivovarov. 2019-02-25. Affine isoperimetric inequalities on flag manifolds. https://doi.org/10.4153/s0008414x23000871

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