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Second Eigenvalue of Schrödinger Operators¶and Mean Curvature (2000)

El Soufi, Ahmad ; Ilias, Saïd

Springer

Communications in mathematical physics 208 (2000), S. 761-770

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract: Let $M$ be a compact immersed submanifold of the Euclidean space, the hyperbolic space or the standard sphere. For any continuous potential q on M, we give a sharp upper bound for the second eigenvalue of the operator −Δ+q in terms of the total mean curvature of M and the mean value of q. Moreover, we analyze the case where this bound is achieved. As a consequence of this result we obtain an alternative proof for the Alikakos–Fusco conjecture concerning the stability of the interface in the Allen–Cahn reaction diffusion model.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002200050009

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