An improved Morse index bound of min–max minimal hypersurfaces
Tóm tắt
In this paper, we give an improved Morse index upper bound for minimal hypersurfaces from Almgren–Pitts min–max construction in any closed Riemannian manifold
$$M^{n+1}$$
$$(n+1 \ge 3$$
), which generalizes a result by Zhou (Ann Math 192(3):767–820, 2020) for
$$3 \le n+1 \le 7$$
. The novel techniques are the construction of hierarchical deformations and a restrictive min–max theory. These techniques do not rely on bumpy metrics, and thus could be adapted to many other min–max settings.
Tài liệu tham khảo
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