A question of Kuhnau

Samuel L. Krushkal

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arXiv · 1808.02845

A question of Kuhnau

Samuel L. Krushkal

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Abstract

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 posed 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 a stronger result for rectangles.

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Samuel L. Krushkal. 2018-08-08. A question of Kuhnau. https://arxiv.org/abs/1808.02845

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