Existence of unstable minimal surfaces in manifolds with homology and applications to triply periodic minimal surfaces. (English) Zbl 0798.53009

Hass, Joel; Pitts, Jon T.; Rubinstein, J. H.

Greene, Robert (ed.) et al., Differential geometry. Part 1: Partial differential equations on manifolds. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 1, 147-162 (1993).

The authors use a minimum/maximum method from the geometric calculus of variations to construct infinite families of minimal surfaces in certain 3-manifolds. Applications are given to “Unstable minimal surfaces in manifolds with homology”, “Unstable minimal surfaces in certain Seifert fiber spaces”, and to the “Existence of triply periodic minimal surfaces” in Euclidean 3-space.
For the entire collection see [Zbl 0773.00022].

Reviewer: M.Grüter (Saarbrücken)

MSC:

53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q10	Optimization of shapes other than minimal surfaces

Keywords:

unstable minimal surfaces; mini-max construction; Seifert fiber spaces; periodic minimal surfaces