论文标题
国旗歧管的刚度
Rigidity of flag manifolds
论文作者
论文摘要
令$ n \ subset gl（n，r）$为对角线上$ 1 $ s的上部三角矩阵组，配备了标准的Carnot组结构。我们表明，当$ n $的开放子集与更普遍的Sobolev映射与非排效机Pansu差异之间的拟声构型同态性质之间是刚性的，当$ n \ geq 4 $时；这解决了此类组的规律性猜想。该结果是从$ r^n $中完整标志的多种标准的刚度定理中得出的。在复杂和四个季节的情况下也有类似的结果。
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.
