[過去ﾛｸﾞ] 「名誉教授」のスレ (1002ﾚｽ)
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689: 2024/08/31(土)07:40 ID:ru1isYd6(1/4) AAS
\section*{\textbf{Automorphisms of noncompact Riemann surfaces}}Noncompact Riemann surfaces are often referred to as open Riemann surfaces. Behnke and Stein [B-S] proved that every open Riemann surface is holomorphically convex. One can prove it by combining Grauert's solution [G] of the Levi problem and a theorem by Greene and Wu in [G-W] asserting that every connected paracompact noncompact complex manifold admits a $C^\infty$ exhaustion function whose complex Hessian has everywhere at least one positive eigenvalue. Namely, Grauert's theorem says that a complex manifold admitting a strictly plurisubharmonic exhaustion function is a Stein manifold (or equivalently biholomorphically equivalent to a closed complex submanifold of $\mathbb{C}^N$) and open Riemann surfaces satisfy this criterion by [G-W] (see also [Oh]).

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691: 2024/08/31(土)10:07 ID:ru1isYd6(2/4) AAS
新しいsectionのタイトルが書けたところ

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694: 2024/08/31(土)21:17 ID:ru1isYd6(3/4) AAS
授業中に言い争いになったことはあるが
何かを投げたことはない

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696: 2024/08/31(土)21:54 ID:ru1isYd6(4/4) AAS
多価関数と言ったら「関数は定義により一価だから多価関数という言い方はやめてくれ」と言われた

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