Genus bounds for min-max minimal surfaces (Q2315245)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Genus bounds for min-max minimal surfaces |
scientific article |
Statements
Genus bounds for min-max minimal surfaces (English)
0 references
2 August 2019
0 references
The author proves optimal genus bounds for minimal surfaces arising from the min-max construction of \textit{F. R. Smith} [On the existence of embedded minimal two spheres in the three sphere, endowed with an arbitrary Riemannian metric. University of Melbourne (PhD thesis) (1982); Theorem 1.2], confirming in this way a conjecture made by \textit{J. T. Pitts} and \textit{J. H. Rubinstein} [Proc. Cent. Math. Anal. Aust. Natl. Univ. 10, 163--176 (1986; Zbl 0602.49028)].
0 references
Heegaard surfaces
0 references
sweepout by Heegaard surfaces
0 references
minimizing sequence
0 references
min-max sequence
0 references
genus bounds
0 references
genus collapse
0 references
layer cake formula
0 references
co area formula
0 references
lifting lemma
0 references
