Open problems on compact constant mean curvature surfaces with boundary

TL;DR

This paper presents a collection of open problems in the theory of compact constant mean curvature surfaces with boundary and surveys the current progress towards solving them.

Contribution

It introduces new open problems in the field and provides a survey of the current status of research on these problems.

Findings

Identification of key open problems in the field.

Summary of current research progress on these problems.

Highlights of challenges and future directions.

Abstract

We present a collection of easily stated open problems in the theory of compact constant mean curvature surfaces with boundary. We also survey the current status of answering them.