Gluing doubly periodic Scherk surfaces into minimal surfaces

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Bibliographic Details
Main Authors:	Chen, Hao, Wu, Yunhua
Format:	Preprint
Published:	2025
Subjects:	Differential Geometry 53A10
Online Access:	Acceder al recurso
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_version_	1866918133953986560
author	Chen, Hao Wu, Yunhua
author_facet	Chen, Hao Wu, Yunhua
contents	We construct minimal surfaces by stacking doubly periodic Scherk surfaces one above another and gluing them along their ends. It is previously known that the Karcher--Meeks--Rosenberg (KMR) doubly periodic minimal surfaces and Meeks' family of triply periodic minimal surfaces can both be obtained by gluing two Scherk surfaces. There have been hope and failed attempts to glue more Scherk surfaces. But our analysis shows that: Except for the special case where the doubly periodic Scherk surfaces all have triangular horizontal lattice, a glue construction can only produce the trivial Scherk surface itself, the KMR examples, or Meeks' surfaces.
format	Preprint
id	arxiv_https___arxiv_org_abs_2507_12859
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Gluing doubly periodic Scherk surfaces into minimal surfaces Chen, Hao Wu, Yunhua Differential Geometry 53A10 We construct minimal surfaces by stacking doubly periodic Scherk surfaces one above another and gluing them along their ends. It is previously known that the Karcher--Meeks--Rosenberg (KMR) doubly periodic minimal surfaces and Meeks' family of triply periodic minimal surfaces can both be obtained by gluing two Scherk surfaces. There have been hope and failed attempts to glue more Scherk surfaces. But our analysis shows that: Except for the special case where the doubly periodic Scherk surfaces all have triangular horizontal lattice, a glue construction can only produce the trivial Scherk surface itself, the KMR examples, or Meeks' surfaces.
title	Gluing doubly periodic Scherk surfaces into minimal surfaces
topic	Differential Geometry 53A10
url	https://arxiv.org/abs/2507.12859

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