Constant mean curvature cylinders with irregular ends

TL;DR

This paper introduces a new class of constant mean curvature cylinders with irregular ends, constructed by unitarizing the monodromy of Hill's equation, expanding the known geometric structures with specified umbilic points.

Contribution

It demonstrates the existence of constant mean curvature cylinders with arbitrary umbilics using monodromy unitarization, a novel approach in differential geometry.

Findings

Existence of new CMC cylinders with irregular ends.

Construction method via monodromy unitarization of Hill's equation.

Potential applications in geometric analysis and surface theory.

Abstract

We prove the existence of a new class of constant mean curvature cylinders with an arbitrary number of umbilics by unitarizing the monodromy of Hill's equation.