A Faber–Krahn Inequality for the Cheeger Constant of $$N$$ N -gons

2014 ◽  
Vol 26 (1) ◽  
pp. 88-117 ◽  
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà
Keyword(s):  
Cheeger Constant ◽  
Krahn Inequality

Reverse Faber–Krahn and Mahler inequalities for the Cheeger constant

2018 ◽  
Vol 148 (5) ◽  
pp. 913-937
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà
Keyword(s):  
Convex Body ◽  
Polar Body ◽  
Convex Bodies ◽  
Type Inequality ◽  
Symmetric Convex ◽  
Cheeger Constant ◽  
Regular Triangle ◽  
Centrally Symmetric ◽  
Affine Image ◽  
Krahn Inequality

We prove a reverse Faber–Krahn inequality for the Cheeger constant, stating that every convex body in ℝ2 has an affine image such that the product between its Cheeger constant and the square root of its area is not larger than the same quantity for the regular triangle. An analogous result holds for centrally symmetric convex bodies with the regular triangle replaced by the square. We also prove a Mahler-type inequality for the Cheeger constant, stating that every axisymmetric convex body in ℝ2 has a linear image such that the product between its Cheeger constant and the Cheeger constant of its polar body is not larger than the same quantity for the square.

Spectral gap of a weighted 3-simplicial complex

2021 ◽  
pp. 2150084
Author(s):  
Khalid Hatim ◽  
Azeddine Baalal
Keyword(s):  
Lower Bound ◽  
Simplicial Complex ◽  
Upper Bound ◽  
Spectral Gap ◽  
Simplicial Complexes ◽  
Cheeger Constant ◽  
Nonzero Eigenvalue ◽  
New Framework

In this paper, we construct a new framework that’s we call the weighted [Formula: see text]-simplicial complex and we define its spectral gap. An upper bound for our spectral gap is given by generalizing the Cheeger constant. The lower bound for our spectral gap is obtained from the first nonzero eigenvalue of the Laplacian acting on the functions of certain weighted [Formula: see text]-simplicial complexes.

scholarly journals Towards a reversed Faber–Krahn inequality for the truncated Laplacian

2019 ◽  
Vol 36 (3) ◽  
pp. 723-740 ◽  
Author(s):  
Isabeau Birindelli ◽  
Giulio Galise ◽  
Hitoshi Ishii
Keyword(s):  
Krahn Inequality

scholarly journals Cheeger Constant and Connectivity of Graphs

2002 ◽  
Vol 8 (2) ◽  
pp. 147-150 ◽  
Author(s):  
Gen-ichi OSHIKIRI
Keyword(s):  
Cheeger Constant

On spectral and boundary properties of the volume potential for the Helmholtz equation

2019 ◽  
Vol 14 (5) ◽  
pp. 502
Author(s):  
Tynysbek Sharipovich Kalmenov ◽  
Michael Ruzhansky ◽  
Durvudkhan Suragan
Keyword(s):  
Helmholtz Equation ◽  
Differential Operators ◽  
Nonlocal Boundary ◽  
Spectral Geometry ◽  
Bessel Potential ◽  
Nonlocal Boundary Value Problem ◽  
Volume Potential ◽  
Potential Operators ◽  
Boundary Properties ◽  
Krahn Inequality

In this paper, we study boundary properties and some questions of spectral geometry for certain volume potential type operators (Bessel potential operators) in an open bounded Euclidean domains. In particular, the results can be valid for differential operators, which are related to a nonlocal boundary value problem for the Helmholtz equation, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of the Rayleigh-Faber-Krahn inequality.

scholarly journals The Cheeger constant of curved tubes

2019 ◽  
Vol 112 (4) ◽  
pp. 429-436 ◽  
Author(s):  
David Krejčiřík ◽  
Gian Paolo Leonardi ◽  
Petr Vlachopulos
Keyword(s):  
Cheeger Constant

scholarly journals Surgery of the Faber–Krahn inequality and applications to heat kernel bounds

2016 ◽  
Vol 131 ◽  
pp. 243-272 ◽  
Author(s):  
Alexander Grigor’yan ◽  
Laurent Saloff-Coste
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds ◽  
Krahn Inequality
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