Annular type surfaces with fixed boundary and with prescribed, almost constant mean curvature

TL;DR

This paper investigates the existence of annular surfaces with nearly constant mean curvature, bounded by coaxial circles, using mathematical analysis of unduloids and nodoids in three-dimensional space.

Contribution

It provides new existence and nonexistence results for specific annular surfaces with prescribed mean curvature in 3, focusing on boundary conditions involving coaxial circles.

Findings

Established conditions for the existence of such surfaces.

Identified scenarios where these surfaces do not exist.

Characterized surfaces as normal graphs of unduloids or nodoids.

Abstract

We prove existence and nonexistence results for annular type parametric surfaces with prescribed, almost constant mean curvature, characterized as normal graphs of compact portions of unduloids or nodoids in $\mathbb{R}^{3}$, and whose boundary consists of two coaxial circles of the same radius.