Rigidity of flag manifolds
| Autor: | Kleiner, Bruce, Muller, Stefan, Xie, Xiangdong |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Added citations to earlier work which had been overlooked in the previous version of the paper |
| Databáze: | arXiv |
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