Extremal properties of eigenvalues for a metric graph

Leonid Friedlander[1]

  • [1] University of Arizona, Department of Mathematics University of Arizona Tucson, AZ 85721 (USA)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 1, page 199-211
  • ISSN: 0373-0956

Abstract

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We establish the sharp lower bound for eigenvalues of a metric graph.

How to cite

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Friedlander, Leonid. "Extremal properties of eigenvalues for a metric graph." Annales de l’institut Fourier 55.1 (2005): 199-211. <http://eudml.org/doc/116184>.

@article{Friedlander2005,
abstract = {We establish the sharp lower bound for eigenvalues of a metric graph.},
affiliation = {University of Arizona, Department of Mathematics University of Arizona Tucson, AZ 85721 (USA)},
author = {Friedlander, Leonid},
journal = {Annales de l’institut Fourier},
keywords = {Eigenvalues; metric graph; symmetrization; eigenvalues},
language = {eng},
number = {1},
pages = {199-211},
publisher = {Association des Annales de l'Institut Fourier},
title = {Extremal properties of eigenvalues for a metric graph},
url = {http://eudml.org/doc/116184},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Friedlander, Leonid
TI - Extremal properties of eigenvalues for a metric graph
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 1
SP - 199
EP - 211
AB - We establish the sharp lower bound for eigenvalues of a metric graph.
LA - eng
KW - Eigenvalues; metric graph; symmetrization; eigenvalues
UR - http://eudml.org/doc/116184
ER -

References

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  1. P. Bérard, Spectral Geometry: Direct and Inverse Problems, 1207 (1986) Zbl0608.58001MR879598
  2. P. Bérard, S. Gallot, Inégalités isopérimétriques pour l'équation de la chaleur et application à l'estimation de quelques invariants, (1983-1984) Zbl0542.53025
  3. S. Gallot, Inégalités isopérimétriques, courbure Ricci et invariants géométriques I, C. R. Acad. Sc. Paris 296 (1983), 333-336 Zbl0535.53034MR697966
  4. S. Gallot, Inégalités isopérimétriques et analytiques sur les variétés rimanniennes, (1988), 163-164 Zbl0674.53001
  5. P. Kuchment, Quantum graphs: I, Some basic structures, Waves Random Media 14 (2004) Zbl1063.81058MR2042548
  6. G. Pólya, G. Szegö, Isoperimetric Inequalities in Mathematical Physics, (1951) Zbl0044.38301MR43486

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