Convergence of spectra of graph-like thin manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F05%3A00032293" target="_blank" >RIV/61389005:_____/05:00032293 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Convergence of spectra of graph-like thin manifolds
Original language description
We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph withKirchhoff boundary conditions at the vertices. On the other hand, if the shrinking at the vertex parts of the manifold is sufficiently slower comparing to that of the edge parts, the limiting spectrum corresponds to decoupled edges with Dirichlet boundary conditions at the endpoints. At the borderline between the two regimes we have a third possibility when the limiting spectrum can be described by a nontrivial coupling at the vertices.
Czech name
Konvergence spekter tenkych variet typu grafu
Czech description
Uvažujeme množinu kompaktních variet, jež kolabuje vzhledem ke vhodnému parametru na graf. Hlavní výsledek je, že spektrum Laplace-Beltramiho operátoru konverguje ke spektru (diferenciélniho)Laplaciánu na grafu s Kirchhoffovými hraničními podmínkami ve vrcholech.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/IAA1048101" target="_blank" >IAA1048101: Quantum graphs and related systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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