リーマン面 (648ﾚｽ)
上下前次1-新
抽出解除 必死ﾁｪｯｶｰ(本家) (べ) 自ID ﾚｽ栞 あぼーん

---

ﾘﾛｰﾄﾞ規制です｡10分ほどで解除するので､他のﾌﾞﾗｳｻﾞへ避難してください｡

---

82: １３２人目の素数さん [] 2024/01/24(水)01:05 ID:1i9Un+hN(1/2)
Introduction
Riemann’s theorem on the negligibility of isolated singularities of
bounded holomorphic functions implies Casorati-Weierstrass theorem
on the behavior of holomorphic functions near essential isolated singularities. To analyse the behavior of
holomorphic functions around　their non-isolated essential singularities for extending the Picard theorem,
function-theoretic null sets had to be studied. Robin constant and
logarithmic capacity are conformal invariants which arose in this context. Later it turned out that
they are also useful for other purposes.
Existence of Evans potentials characterizes the class of Riemann surfaces with “null-boundary”.
Construction of functions of Evans type
by Nakai has an application to a question in several complex variables.

---

86: １３２人目の素数さん [] 2024/01/24(水)20:26 ID:1i9Un+hN(2/2)
The purpose of this section is to give an account for the construction of canonical potential functions on plane domains based on the
equivalence of the logarithmic capacity and the transcendental diameter, which can be generalized on Riemann surfaces. Roughly speaking,
the notions of logarithmic capacity and transcendental diameter are
refinements of the one dimensional Hausdorff measure.
Extensions of Picard’s theorem have been obtained in order to describe the essential singularities of meromorphic functions near the sets
of null capacity. As a typical result, see [Km] for instance.

[Km] Kametani, S. On Hausdorff ’s measures and generalized capacities with some
of their applications to the theory of functions, Jap. Journ. Math., 19 (1944–48),
pp. 217-257.

---

上下前次1-新書関写板覧索設栞歴

---

ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ

---

ぬこの手 ぬこTOP 0.027s