Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces

Author(s)

Gorodski, Claudio ^[1] ; Mendes, Ricardo A. E. ^[2] ; Radeschi, Marco ^[3]

Affiliation

^[1] Univ Sao Paulo, Sao Paulo - Brazil

^[2] Univ Cologne, Cologne - Germany

^[3] Univ Notre Dame, Notre Dame, IN 46556 - USA

• Document type: Journal article
• Source: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 58, n. 4 AUG 2019.
• Web of Science Citations: 0

Abstract

We find many examples of compact Riemannian manifolds (M,g) whose closed minimal hypersurfaces satisfy a lower bound on their index that is linear in their first Betti number. Moreover, we show that these bounds remain valid when the metric g is replaced with g in a neighbourhood of g. Our examples (M,g) consist of certain minimal isoparametric hypersurfaces of spheres, their focal manifolds, the Lie groups SU(n) for n17 and Sp(n) for all n, and all quaternionic Grassmannians. (AU)

• FAPESP's process: 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis
• Grantee: Paolo Piccione
• Support Opportunities: Research Projects - Thematic Grants