The Jacobi operator of some special minimal hypersurfaces

In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in Rᵐ× Rⁿ with m,n≥ 2. These hypersurfaces are asymptotic at infinity to a fixed Lawson cone Cm,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.