2019/01/17 by Andreas Fuchs, Fuchs, Andreas
Mathematics · #35B40 #51B10 #58J72 #58K10 #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1901.05774
openalex publication_date 2019/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider those simply connected isothermic surfaces for which their Hopf differential factorizes into a real function and a meromorphic quadratic differential that has a zero or pole at some point, but is nowhere zero and holomorphic otherwise. Upon restriction to a simply connected patch that does not contain the zero or pole, the Darboux and Calapso transformations yield new isothermic surfaces. We determine the limiting behaviour of these transformed patches as the zero or pole of the meromorphic quadratic differential is approached and investigate whether they are continuous around that point.