Counterexample to a conjecture of H. Hopf

1986/01/01 by Henry C. Wente · 6 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Analytic and geometric function theory #Advanced Mathematical Modeling in Engineering #Counterexample #Mathematics #Conjecture #Pure mathematics #Combinatorics

paper · pdf · doi:10.2140/pjm.1986.121.193

openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

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.

Citations

• A symmetry problem in potential theory

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