论文标题
全体形态图的切片刚度特性Kobayashi-Imetrymotormoticaly在复杂的测量学上保存
Slice rigidity property of holomorphic maps Kobayashi-isometrically preserving complex geodesics
论文作者
论文摘要
在本文中，我们研究以下“切片刚度”：给定两个kobayashi完整的双曲歧管$ m，n $和一系列复杂的大地测量公司$ \ Mathcal f $ $ $ m $的$ m $，当每个holomorphic map $ f：m f：m f：m f：m f：m f n $ to n $ to n $在$上添加了每一个$ $ $ $ \ n $ \ nater $ \ nath $ \ nathcal f $ hosevers $ \ nathcal f $ n os \ nathcal f $生物形态？除其他事项外，我们证明，如果$ m，n $严格（线性）凸面域的平滑界限，$ \ MATHCAL F $的每个元素都包含$ \ Overline {M} $和$ \ Mathcal F $跨度所有$ m $的给定点。尺寸$ 2 $和单位球提供了更多一般结果。
In this paper we study the following "slice rigidity property": given two Kobayashi complete hyperbolic manifolds $M, N$ and a collection of complex geodesics $\mathcal F$ of $M$, when is it true that every holomorphic map $F:M\to N$ which maps isometrically every complex geodesic of $\mathcal F$ onto a complex geodesic of $N$ is a biholomorphism? Among other things, we prove that this is the case if $M, N$ are smooth bounded strictly (linearly) convex domains, every element of $\mathcal F$ contains a given point of $\overline{M}$ and $\mathcal F$ spans all of $M$. More general results are provided in dimension $2$ and for the unit ball.
