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arXiv · 2201.01648

Rigidity of flag manifolds

Bruce Kleiner·Stefan Muller·Xiangdong Xie
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Abstract

Let $N\subset GL(n,R)$ be the group of upper triangular matrices with $1$s on the diagonal, equipped with the standard Carnot group structure. We show that quasiconformal homeomorphisms between open subsets of $N$, and more generally Sobolev mappings with nondegenerate Pansu differential, are rigid when $n \geq 4$; this settles the Regularity Conjecture for such groups. This result is deduced from a rigidity theorem for the manifold of complete flags in $R^n$. Similar results also hold in the complex and quaternion cases.

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Bruce Kleiner, Stefan Muller, Xiangdong Xie. 2022-01-05. Rigidity of flag manifolds. https://arxiv.org/abs/2201.01648

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