球凸函数的Schwarz引理的几何版本

IF 0.6 3区数学 Q3 MATHEMATICS Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-04-04 DOI:10.4153/S0008414X22000529

Maria Kourou, Oliver Roth

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引用次数: 0

摘要

摘要本文证明了单位圆盘上定义的球凸函数的几个尖锐畸变定理和单调性定理，这些函数涉及球长、球面积和球总曲率等几何量。这些结果可以看作是球凸函数的经典Schwarz引理的几何变体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Geometric versions of Schwarz’s lemma for spherically convex functions

Abstract We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area, and total spherical curvature. These results can be viewed as geometric variants of the classical Schwarz lemma for spherically convex functions.

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来源期刊

Canadian Journal of Mathematics-Journal Canadien De Mathematiques 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year. To be submitted to the Journal, papers should be at least 18 pages long and may be written in English or in French. Shorter papers should be submitted to the Canadian Mathematical Bulletin. Le Journal canadien de mathématiques (JCM) publie des articles de recherche innovants de grande qualité dans toutes les branches des mathématiques. Publication phare de la Société mathématique du Canada, il est publié en continu depuis 1949. En ligne, la revue propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés six fois par année. Les textes présentés au JCM doivent compter au moins 18 pages et être rédigés en anglais ou en français. C’est le Bulletin canadien de mathématiques qui reçoit les articles plus courts.