A question of Kuhnau

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Krushkal, Samuel L.^1,2 

[1] Bar Ilan Univ, Dept Math, IL-5290002 Ramat Gan, Israel

[2] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

关键词: Holomorphic quadratic differential;    Teichmuller extremality;    Generalized Gaussian curvature;    Convex quadrilateral;    Beltrami coefficient;   

DOI  :  10.1016/j.jmaa.2018.12.053

来源: Elsevier

【 摘 要 】

It is well known that the square is not a Strebel's point (i.e., its extremal Beltrami coefficient is not Teichmuller). Many years ago, Reiner Kuhnau raised the question: does there exist in the case of a long rectangle the corresponding holomorphic quadratic differential? We prove that the answer is negative for any bounded convex quadrilateral and establish for rectangles a stronger result. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free