An end-to-end construction for compact constant mean curvature surfaces

Mohamed Jleli and Frank Pacard

Vol. 221 (2005), No. 1, 81–108

DOI: 10.2140/pjm.2005.221.81

Abstract

We provide a construction for new compact surfaces of constant mean curvature of genus 3 and higher, based on tools developed for the understanding of complete noncompact constant mean curvature surfaces and the end-to-end construction developed by J. Ratskin to connect (and produce) complete noncompact constant mean curvature surfaces along their ends.

Keywords

compact constant mean curvature surfaces

Mathematical Subject Classification 2000

Primary: 53A10, 53C42, 53C21

Milestones

Received: 16 October 2003

Revised: 1 October 2004

Accepted: 30 November 2004

Published: 1 September 2005