Genus bounds for minimal surfaces arising from min-max constructions. (English) Zbl 1201.53009

In [The min-max construction of minimal surfaces. Harvard University, Cambridge, MA, USA, May 3–5, 2002. Somerville, MA: International Press. Surv. Differ. Geom. 8, 75–107 (2003; Zbl 1051.53052)], T. H. Colding and the first author gave a survey on constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min-max arguments. In this paper, the authors complete the survey by giving genus hounds for the final min-max surface.


53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature


Zbl 1051.53052
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[1] DOI: 10.1007/BF01425476 · Zbl 0339.49020
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