Embedded minimal surfaces in three-manifolds with positive scalar curvature. (English) Zbl 0584.53004

Rubinstein, J. H.

Proc. Am. Math. Soc. 95, 458-462 (1985).

Let M be a closed orientable Riemannian three-manifold with positive scalar curvature. We prove that any embedded closed minimal surface in M has a topological description as a generalized Heegaard surface. Also an existence theorem is proved which gives examples of such minimal surfaces.

MSC:

53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

three-manifold; positive scalar curvature; minimal surface; Heegaard surface