Conformal equivalence of visual metrics in pseudoconvex domains
Conformal equivalence of visual metrics in pseudoconvex domains
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DOI：
10.1007/s00208-020-01962-1
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发表时间：
2017-03
影响因子：
1.4
通讯作者：
L. Capogna;Enrico Le Donne
中科院分区：
文献类型：
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作者：
L. Capogna;Enrico Le Donne
我们改进了Balogh和Bonk提出的估计，证明了有界光滑强伪凸域之间的等距的边界扩张关于Levi形式诱导的次黎曼度量是共形的.作为推论，我们得到了February man关于有界光滑伪凸域间双全纯映射的光滑扩张的一个结果的另一种证明。证据的灵感来自于莫斯托的证明他的刚性定理，是基于渐近双曲字符的小林或伯格曼度量和邦克-施拉姆双曲填充。
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains inare conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between bounded smooth pseudoconvex domains. The proofs are inspired by Mostow’s proof of his rigidity theorem and are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the Bonk-Schramm hyperbolic fillings.