An improved Morse index bound of min-max minimal hypersurfaces (Q6107064)

The celebrated result [\textit{X. Zhou}, Ann. Math. (2), No. 3, 767--820 (2020; Zbl 1461.53051)] establishes an upper bound for minimal hypersurfaces from Almgren-Pitts min-max construction in any closed Riemannian manifold \(M^{n+1}\) with \(n+1\in[3,7]\). The present paper extends the result to any \(n+1\ge 3\) (ref.\ Theorem~1.3). The main techniques are the construction of hierarchical deformations, and a restrictive min-max theory not relying on bumpy metrics.