B. Helffer, A. Morame
Magnetic bottles for the Neumann problem: 
curvature effects in the case of dimension 3
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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.