Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces

2024/10/15 by Toru Kajigaya, Kajigaya, Toru, Keita Kunikawa +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2410.11585

openalex publication_date 2024/10/15 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28

Abstract

We show that the Morse index of unstable closed minimal hypersurface Σ in a compact semi-simple Riemannian symmetric space M=G/K is bounded from below by constant times the first Betti number of Σ. Our proof is based on a natural extension of the previous method and this also provides a novel approach for the index estimate.

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