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Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets
The spectral gap of graphs and Steklov eigenvalues on surfaces
1. | Université de Neuchâtel, Institut de Mathématiques, Rue Emile-Argand 11, Case postale 158, 2009 Neuchâtel, Switzerland |
2. | Département de mathématiques et de statistique, Université Laval, Pavillon Alexandre- Vachon, 1045, av. de la Médecine, Quebec Qc G1V 0A6, Canada |
References:
[1] |
R. Bañuelos, T. Kulczycki, I. Polterovich and B. Siudeja, Eigenvalue inequalities for mixed Steklov problems, in Operator Theory and its Applications, Amer. Math. Soc. Transl. Ser. 2, 231, Amer. Math. Soc., Providence, RI, 2010, 19-34. |
[2] |
R. Brooks, The first eigenvalue in a tower of coverings, Bull. Amer. Math. Soc. (N.S.), 13 (1985), 137-140.
doi: 10.1090/S0273-0979-1985-15397-2. |
[3] |
R. Brooks, The spectral geometry of a tower of coverings, J. Differential Geom., 23 (1986), 97-107. |
[4] |
M. Burger, Estimation de petites valeurs propres du laplacien d'un revêtement de variétés riemanniennes compactes, C. R. Acad. Sci. Paris Sér. I Math., 302 (1986), 191-194. |
[5] |
P. Buser, On the bipartition of graphs, Discrete Appl. Math., 9 (1984), 105-109.
doi: 10.1016/0166-218X(84)90093-3. |
[6] |
F. R. K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, No. 92, American Mathematical Society, Providence, RI, 1997. |
[7] |
B. Colbois, A. El Soufi and A. Girouard, Isoperimetric control of the Steklov spectrum, J. Funct. Anal., 261 (2011), 1384-1399.
doi: 10.1016/j.jfa.2011.05.006. |
[8] |
B. Colbois and A.-M. Matei, On the optimality of J. Cheeger and P. Buser inequalities, Differential Geom. Appl., 19 (2003), 281-293.
doi: 10.1016/S0926-2245(03)00035-4. |
[9] |
A. Fraser and R. Schoen, Sharp eigenvalue bounds and minimal surfaces in the ball, arXiv:1209.3789, (2013). |
[10] |
A. Girouard and I. Polterovich, Upper bounds for Steklov eigenvalues on surfaces, Electron. Res. Announc. Math. Sci., 19 (2012), 77-85.
doi: 10.3934/era.2012.19.77. |
[11] |
S. Hoory, N. Linial and A. Wigderson, Expander graphs and their applications, Bull. Amer. Math. Soc. (N.S.), 43 (2006), 439-561 (electronic).
doi: 10.1090/S0273-0979-06-01126-8. |
[12] |
M. Karpukhin, Large Steklov and Laplace eigenvalues,, in preparation., ().
|
[13] |
G. Kokarev, Variational aspects of Laplace eigenvalues on Riemannian surfaces, arXiv:1103.2448, (2011). |
[14] |
N. N. Moiseev, Introduction to the theory of oscillations of liquid-containing bodies, in Advances in Applied Mechanics, Vol. 8, Academic Press, New York, 1964, 233-289. |
[15] |
M. S. Pinsker, On the complexity of a concentrator, in 7th International Teletraffic Conference, 1973, 318/1-318/4. |
[16] |
P. C. Yang and S. T. Yau, Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 7 (1980), 55-63. |
show all references
References:
[1] |
R. Bañuelos, T. Kulczycki, I. Polterovich and B. Siudeja, Eigenvalue inequalities for mixed Steklov problems, in Operator Theory and its Applications, Amer. Math. Soc. Transl. Ser. 2, 231, Amer. Math. Soc., Providence, RI, 2010, 19-34. |
[2] |
R. Brooks, The first eigenvalue in a tower of coverings, Bull. Amer. Math. Soc. (N.S.), 13 (1985), 137-140.
doi: 10.1090/S0273-0979-1985-15397-2. |
[3] |
R. Brooks, The spectral geometry of a tower of coverings, J. Differential Geom., 23 (1986), 97-107. |
[4] |
M. Burger, Estimation de petites valeurs propres du laplacien d'un revêtement de variétés riemanniennes compactes, C. R. Acad. Sci. Paris Sér. I Math., 302 (1986), 191-194. |
[5] |
P. Buser, On the bipartition of graphs, Discrete Appl. Math., 9 (1984), 105-109.
doi: 10.1016/0166-218X(84)90093-3. |
[6] |
F. R. K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, No. 92, American Mathematical Society, Providence, RI, 1997. |
[7] |
B. Colbois, A. El Soufi and A. Girouard, Isoperimetric control of the Steklov spectrum, J. Funct. Anal., 261 (2011), 1384-1399.
doi: 10.1016/j.jfa.2011.05.006. |
[8] |
B. Colbois and A.-M. Matei, On the optimality of J. Cheeger and P. Buser inequalities, Differential Geom. Appl., 19 (2003), 281-293.
doi: 10.1016/S0926-2245(03)00035-4. |
[9] |
A. Fraser and R. Schoen, Sharp eigenvalue bounds and minimal surfaces in the ball, arXiv:1209.3789, (2013). |
[10] |
A. Girouard and I. Polterovich, Upper bounds for Steklov eigenvalues on surfaces, Electron. Res. Announc. Math. Sci., 19 (2012), 77-85.
doi: 10.3934/era.2012.19.77. |
[11] |
S. Hoory, N. Linial and A. Wigderson, Expander graphs and their applications, Bull. Amer. Math. Soc. (N.S.), 43 (2006), 439-561 (electronic).
doi: 10.1090/S0273-0979-06-01126-8. |
[12] |
M. Karpukhin, Large Steklov and Laplace eigenvalues,, in preparation., ().
|
[13] |
G. Kokarev, Variational aspects of Laplace eigenvalues on Riemannian surfaces, arXiv:1103.2448, (2011). |
[14] |
N. N. Moiseev, Introduction to the theory of oscillations of liquid-containing bodies, in Advances in Applied Mechanics, Vol. 8, Academic Press, New York, 1964, 233-289. |
[15] |
M. S. Pinsker, On the complexity of a concentrator, in 7th International Teletraffic Conference, 1973, 318/1-318/4. |
[16] |
P. C. Yang and S. T. Yau, Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 7 (1980), 55-63. |
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