01-362 B. Helffer, A. Morame
Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3 (175K, LaTeX 2e) Oct 10, 01
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Abstract. In a previous work, we have analyzed the recent results obtained on the Neumann realization of the Schr\"odinger operator in the case of dimension 3 by Lu and Pan. After presenting a short treatment of their spectral analysis of key-models, we show briefly how to implement the techniques of Helffer-Morame in order to give some localization of the ground state. This leaves open the question of the localization by curvature effect which was conjectured by Bernoff-Sternberg in the case of dimension $2$ and solved by K. Lu and X-B. Pan, M. del Pino, P.L. Felmer and P. Sternberg, and ourselves. We shall now analyze the curvature effects in the case of dimension 3.

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