Geodesic
Absolute continuity of the spectrum of the periodic Scr\"odinger operator in a~layer and in a~smooth cylinder
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 69-82

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The Schrödinger operator $H=\Delta+V$ in a layer or in a $d$-dimensional cylinder is considered. The function $V$ is suppored to be periodic with respect to some lattice. The absolute continuity of the spectrum of $H$ is established under the following conditions: $V\in L_{p,\mathrm{loc})}$ where $p>d/2$ in the case of a layer, and $p>>\max(d/2,d-2)$ in the case of a cylinder. Bibl. 14 titles. 
@article{ZNSL_2010_385_a3,
     author = {I. Kachkovskii and N. Filonov},
     title = {Absolute continuity of the spectrum of the periodic {Scr\"odinger} operator in a~layer and in a~smooth cylinder},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {69--82},
     publisher = {mathdoc},
     volume = {385},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a3/}
}
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I. Kachkovskii; N. Filonov. Absolute continuity of the spectrum of the periodic Scr\"odinger operator in a~layer and in a~smooth cylinder. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 69-82. http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a3/