For closed surfaces with nonpositive Euler characteristic fully immersed in S^n, the second Jacobi eigenvalue satisfies λ2 ≤ -2, with equality only for the Clifford torus in S^3 or the equilateral torus in S^5; in S1(r) × S2(s) with r ≥ s, the bound is λ2 ≤ 0, with equality only for the totally…
Alikakos and Giorgio Fusco, The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions, Indiana Univ
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Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator
For closed surfaces with nonpositive Euler characteristic fully immersed in S^n, the second Jacobi eigenvalue satisfies λ2 ≤ -2, with equality only for the Clifford torus in S^3 or the equilateral torus in S^5; in S1(r) × S2(s) with r ≥ s, the bound is λ2 ≤ 0, with equality only for the totally…