Vol. 111, No. 1, 1984

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Complete area minimizing minimal surfaces which are not totally geodesic

Joel Hass

Vol. 111 (1984), No. 1, 35–38
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
Authors
Joel Hass
Mathematics Department
University of California at Davis
Davis CA 95616
United States