Non-degeneracy of Critical Points of the Squared Norm of the Second Fundamental Form on Manifolds with Minimal Boundary

Let ( M , g ¯ ) be a compact Riemannian manifold with minimal boundary such that the second fundamental form is nowhere vanishing on ∂ M . We show that for a generic Riemannian metric g ¯ , the squared norm of the second fundamental form is a Morse function, i.e. all its critical points are non-dege...

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Bibliographic Details
Published in:The Journal of geometric analysis 2023-10, Vol.33 (10), Article 332
Main Authors: Cruz-Blázquez, Sergio, Pistoia, Angela
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Critical point
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Riemann manifold
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Summary:Let ( M , g ¯ ) be a compact Riemannian manifold with minimal boundary such that the second fundamental form is nowhere vanishing on ∂ M . We show that for a generic Riemannian metric g ¯ , the squared norm of the second fundamental form is a Morse function, i.e. all its critical points are non-degenerate. We show that the generality of this property holds when we restrict ourselves to the conformal class of the initial metric on M .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01395-7