The Jacobi operator of some special minimal hypersurfaces

2024/08/16 by Oscar Agudelo, Matteo Rizzi, Agudelo, Oscar +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2408.08728

Abstract

In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in ℝ^m× ℝⁿ with m,n≥ 2. These hypersurfaces are asymptotic at infinity to a fixed Lawson cone C_m,n. In the case m+n≥ 8, we show that such hypersurfaces are strictly stable and we provide a full classification of their bounded Jacobi fields, which in turn allows us to prove the non-degeneracy of such surfaces. In the case m+n≤ 7, we prove that such hypersurfaces have infinite Morse index.

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