On constant mean curvature surfaces satisfying integrable boundary conditions

TL;DR

This paper investigates constant mean curvature surfaces with integrable boundary conditions, deriving potentials for their generalized Weierstrass representation to understand their geometric properties.

Contribution

It introduces a framework for analyzing constant mean curvature surfaces with integrable boundary conditions using the generalized Weierstrass representation.

Findings

Derived potentials for the generalized Weierstrass representation.

Characterized the local theory of such surfaces with boundary conditions.

Provided insights into the geometric structure of these surfaces.

Abstract

We consider the local theory of constant mean curvature surfaces that satisfy one or two integrable boundary conditions and determine the corresponding potentials for the generalized Weierstrass representation.