2 papers
math.AG2025
Universal Deformations of a Curve and a Differential
Emma Carberry, Martin Ulrich Schmidt
We construct universal local deformations (Kuranishi families) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar,…
math.DG2024
Solutions of the Sinh-Gordon Equation of Spectral Genus Two and constrained Willmore Tori I
Markus Knopf, Ricardo Pena Hoepner, Martin U. Schmidt
We investigate solutions of the elliptic sinh-Gordon equation of spectral genus g<3. These solutions are parametrized by complex matrix-valued polynomials called potentials. On the…