AI 中文总结
该研究证明了保持Kobayashi距离的从单位圆盘D到对称双圆盘G₂的映射f必为全纯或反全纯，完善了对称双圆盘上等距映射的相关理论。
AI 中文摘要
我们证明，每个保持Kobayashi距离的映射f：D→G₂都是全纯的或反全纯的。
英文摘要
We prove that every map $f:U\to\GG$ preserving the Poincaré distance and the Kobayashi distance is holomorphic or anti-holomorphic, where $U$ is a connected open subset of the unit disc. We also study the nonroyal automorphism orbits of $\GG$. A $C^1$ map on a connected relatively open part of such an orbit which preserves the restriction of the ambient Kobayashi--Royden metric is the restriction of a global automorphism or anti-automorphism of $\GG$. The same conclusion holds for maps preserving the ambient Kobayashi distance.
