Morse index of multiplicity one min-max minimal hypersurfaces

Fernando C. Marques; André Neves

doi:10.1016/j.aim.2020.107527

Morse index of multiplicity one min-max minimal hypersurfaces

Fernando C. Marques, André Neves

Mathematics

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52 Scopus citations

Abstract

In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the families used in the construction. This confirms part of the program ([31], [34], [36], [43]) proposed by the authors with the goal of developing a Morse theory for the area functional.

Original language	English (US)
Article number	107527
Journal	Advances in Mathematics
Volume	378
DOIs	https://doi.org/10.1016/j.aim.2020.107527
State	Published - Feb 12 2021

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Min-max methods
Minimal surfaces
Morse Index

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10.1016/j.aim.2020.107527

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title = "Morse index of multiplicity one min-max minimal hypersurfaces",

abstract = "In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the families used in the construction. This confirms part of the program ([31], [34], [36], [43]) proposed by the authors with the goal of developing a Morse theory for the area functional.",

keywords = "Min-max methods, Minimal surfaces, Morse Index",

author = "Marques, \{Fernando C.\} and Andr{\'e} Neves",

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year = "2021",

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AU - Neves, André

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N2 - In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the families used in the construction. This confirms part of the program ([31], [34], [36], [43]) proposed by the authors with the goal of developing a Morse theory for the area functional.

AB - In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the families used in the construction. This confirms part of the program ([31], [34], [36], [43]) proposed by the authors with the goal of developing a Morse theory for the area functional.

KW - Min-max methods

KW - Minimal surfaces

KW - Morse Index

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U2 - 10.1016/j.aim.2020.107527

DO - 10.1016/j.aim.2020.107527

M3 - Article

AN - SCOPUS:85098179336

SN - 0001-8708

VL - 378

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 107527

ER -

Morse index of multiplicity one min-max minimal hypersurfaces

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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