Limit lamination theorems for H-surfaces

TL;DR

This paper establishes general theorems on the limits of sequences of constant mean curvature surfaces with fixed genus in three-dimensional space, extending previous minimal surface results to non-zero mean curvature cases.

Contribution

It generalizes structure theorems for minimal surfaces to constant mean curvature surfaces, providing new insights into their lamination limits.

Findings

Proves limit lamination theorems for H-surfaces with fixed genus.

Extends structure theorems to non-zero constant mean curvature surfaces.

Analyzes behavior of surfaces as boundaries tend to infinity.

Abstract

In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces $M_n$ embedded in $\mathbb R^3$ with constant mean curvature $H_n$ and fixed finite genus, when the boundaries of these surfaces tend to infinity. Two of these theorems generalize to the non-zero constant mean curvature case, similar structure theorems by Colding and Minicozzi in~[6,8] for limits of sequences of minimal surfaces of fixed finite genus.