Complete area minimizing minimal surfaces which are not totally geodesic

Joel Hass

Vol. 111 (1984), No. 1, 35–38

DOI: 10.2140/pjm.1984.111.35

Abstract

If a 3-manifold has non-negative Ricci curvature, then a complete area minimizing minimal surface in the 3-manifold is totally geodesic. The main theorem gives a method of constructing non-totally geodesic examples of such surfaces in certain manifolds which do not satisfy the Ricci curvature conditions. In particular, examples are described for hyperbolic space.

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 53C42, 58E12

Milestones

Received: 5 October 1982

Published: 1 March 1984