Abstract:The singly periodic Scherk surfaces with higher dihedral symmetry have 2n-ends that come together based upon the value of '. These surfaces are embedded provided that 2 n < n 1 n ' < 2. Previously, this inequality has been proved by turning the problem into a Plateau problem and solving, and by using the Jenkins-Serrin solution and Krust's theorem. In this paper we provide a proof of the embeddedness of these surfaces by using some results about univalent planar harmonic mappings from geometric function theory… Show more
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