On a convexity property of the space of almost fuchsian immersions

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2023-11-28 DOI:10.1007/s10711-023-00865-0

Samuel Bronstein, Graham Andrew Smith

引用次数: 0

Abstract

We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of the immersion at any given point is a concave function of the Hopf differential. As a consequence, we show that the set of all such Hopf differentials is a convex subset of the space of holomorphic quadratic differentials of the surface. In addition, we address the non-equivariant case, and obtain lower and upper bounds for the size of this set.

查看原文本刊更多论文

关于几乎紫红色浸没空间的凸性

研究紧致黎曼曲面的几乎紫红色极小浸入的Hopf微分空间。我们证明了在任何给定点的浸入的外在曲率是Hopf微分的凹函数。因此，我们证明了所有这些Hopf微分的集合是曲面的全纯二次微分空间的凸子集。此外，我们讨论了非等变情况，并得到了该集合大小的下界和上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.