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Morse index and multiplicity of min-max minimal hypersurfaces

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arxiv 1512.06460 v2 pith:JWKRM7XY submitted 2015-12-20 math.DG math.AP

Fernando C. Marques , André Neves This is my paper · ORCID
classification math.DGmath.AP
keywords indexmin-maxminimalmorsehypersurfacesmultiplicitytheoryadvance
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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 min-max 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.

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  1. The p-widths of $RP^2$

    math.DG 2025-01 conditional novelty 6.0 of 10

    The p-widths of (RP^2, g_std) are ω_p = 2π floor((1+sqrt(1+8p))/4), achieved by Z2-invariant polynomial sweepouts.

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