Globally subanalytic CMC surfaces in $\mathbb{R}^3$

TL;DR

This paper classifies globally subanalytic constant mean curvature (CMC) surfaces in three-dimensional space, showing they are limited to planes, spheres, or cylinders, thus providing a complete geometric characterization.

Contribution

It establishes a classification result for globally subanalytic CMC surfaces, identifying all possible shapes as planes, spheres, or cylinders.

Findings

Globally subanalytic CMC surfaces are only planes, spheres, or cylinders.

The classification is complete for nonsingular cases.

The result narrows the scope of possible geometries under subanalytic conditions.

Abstract

We prove that globally subanalytic nonsingular CMC surfaces of $\mathbb{R}^3$ are only planes, round spheres or right circular cylinders