Existence of regular neighborhoods for H-surfaces

TL;DR

This paper investigates the global geometry of complete constant mean curvature hypersurfaces, establishing conditions for properness and proving the existence of regular neighborhoods in specific manifolds.

Contribution

It introduces new conditions ensuring properness and demonstrates the existence of regular neighborhoods for certain H-surfaces in n-manifolds.

Findings

Conditions for properness of H-surfaces

Existence of fixed size one-sided regular neighborhoods

Applicability to specific n-manifolds

Abstract

In this paper, we study the global geometry of complete, constant mean curvature hypersurfaces embedded in n-manifolds. More precisely, we give conditions that imply properness of such surfaces and prove the existence of fixed size one-sided regular neighborhoods for certain constant mean curvature hypersurfaces in certain n-manifolds.