Minimal surfaces and the topology of three-manifolds. (English) Zbl 1100.57021

Hass, Joel

Hoffman, David (ed.), Global theory of minimal surfaces. Proceedings of the Clay Mathematics Institute 2001 summer school, Berkeley, CA, USA, June 25–July 27, 2001. Providence, RI: American Mathematical Society (AMS). Cambridge, MA: Clay Mathematics Institute (ISBN 0-8218-3587-4/pbk). Clay Mathematics Proceedings 2, 705-724 (2005).

Summary: This article based on three lectures given at MSRI in July 2001, discusses old and new results relating minimal surface theory and the topology of 3-manifolds. The goal is to give a picture of how minimal surfaces have become an important tool in the study of 3-manifold.
For the entire collection see [Zbl 1078.53002].

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
57-02	Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
68Q25	Analysis of algorithms and problem complexity

Keywords:

minimal surface; 3-manifold; complexity of algorithms; normal surface; area