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Morse index and multiplicity of min-max minimal hypersurfaces

Author(s): Coda Marques, Fernando; Neves, André

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Abstract: The Min-max Theory for the area functional, started by Almgren in the early 1960s and greatly improved by Pitts in 1981, was left incomplete because it gave no Morse index estimate for the minmax minimal hypersurface. We advance the theory further and prove the first general Morse index bounds for minimal hypersurfaces produced by it. We also settle the multiplicity problem for the classical case of one-parameter sweepouts.
Publication Date: 2016
Electronic Publication Date: 2016
Citation: Marques, Fernando C, Neves, André. (2016). Morse index and multiplicity of min-max minimal hypersurfaces. Cambridge Journal of Mathematics, 4 (4), 463 - 511. doi:10.4310/CJM.2016.v4.n4.a2
DOI: doi:10.4310/CJM.2016.v4.n4.a2
ISSN: 2168-0930
EISSN: 2168-0949
Pages: 463 - 511
Type of Material: Journal Article
Journal/Proceeding Title: Cambridge Journal of Mathematics
Version: Author's manuscript

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