Morse index and multiplicity of min-max minimal hypersurfaces
Morse index and multiplicity of min-max minimal hypersurfaces
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 …