Rigidity of groups of circle diffeomorphisms and teichmüller spaces
Rigidity of groups of circle diffeomorphisms and teichmüller spaces
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DOI：
10.1007/s11854-020-0095-6
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发表时间：
2020-03
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通讯作者：
Katsuhiko Matsuzaki
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作者：
Katsuhiko Matsuzaki
在拟共形Teichmüller理论的框架下，研究了一类具有Hölder连续导数的圆同胚的变形，并证明了在圆的对称同胚的共轭下的刚性.作为应用，我们给出了这样一个群同态群与一个Möbius群通过一个具有相同正则性的群同态共轭的一个条件.该策略是找到一个等距作用在可积Teichmüller空间上的具有Weil-Petersson度量的群的不动点。
We consider deformations of a group of circle diffeomorphisms with Hölder continuous derivative in the framework of quasiconformal Teichmüller theory and showcertain rigidity under conjugation by symmetric homeomorphisms of the circle. As an application, we give a condition for such a diffeomorphism group to be conjugate to a Möbius group by a diffeomorphism of the same regularity. The strategy is to find a fixed point of the group which acts isometrically on the integrable Teichmüller space with the Weil–Petersson metric.