Counterexample to a conjecture of H. Hopf

Henry Wente

Vol. 121 (1986), No. 1, 193–243

DOI: 10.2140/pjm.1986.121.193

Abstract

The purpose of this paper is to produce an immersion of a compact oriented two-dimensional surface of genus one into Euclidean 3-space with constant mean curvature H≠0. We thus provide a counterexample in dimension 3 to the following conjecture of H. Hopf.

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 53C42

Milestones

Received: 8 August 1984

Published: 1 January 1986