Take some self map on the unit disk , . If , has a removable singularity at . On , , and with the maximum principle on , we derive everywhere. In particular, if anywhere, constancy by the maximum principle tells us that , where . with the removable singularity removed has , so again, by the maximum principle, means is a constant of modulus . Moreover, if is not an automorphism, we cannot have anywhere, so in that case, .
Variants of the Schwarz lemma
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昨晚，我想起了大挪威数学家 Atle Selberg。他是个很有趣的人，好像在 1943 年挪威被纳粹德国占领时获得了奥斯陆大学的博士。好像他还参军了，也坐牢了。对于他的