Results 31 to 40 of about 358 (72)

On Pleijel's nodal domain theorem [PDF]

arXiv, 2013
A slight improvement of Pleijel's estimate on the number of nodal domains is obtained, exploiting a refinement of the Faber-Krahn inequality and packing density of discs.
arxiv  

Birkhoff Normal Forms in Semi-Classical Inverse Problems [PDF]

arXiv, 2002
We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.
arxiv  

On nodal lines of Neumann eigenfunctions [PDF]

arXiv, 2002
We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain. The technique is based on the `mirror coupling' of reflected Brownian motions.
arxiv  

The "hot spots" problem in planar domains with one hole [PDF]

arXiv, 2004
There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.
arxiv  

Some Asymptotic Behavior of the first Eigenvalue along the Ricci Flow [PDF]

arXiv, 2007
We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.
arxiv  

Neumann spectral cluster estimates outside convex obstacles [PDF]

arXiv, 2010
This paper concerns spectral clusters of the Neumann Laplacian on compact Riemannian manifolds with strictly geodesically concave boundary. We prove an inequality which controls the $L^p$ norms of spectral clusters.
arxiv  

On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori

, 2015
In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tori. We present two results.
Léna, Corentin
core  

Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold [PDF]

, 2007
For any bounded regular domain $\Omega$ of a real analytic Riemannian manifold $M$, we denote by $\lambda_{k}(\Omega)$ the $k$-th eigenvalue of the Dirichlet Laplacian of $\Omega$.
Ilias, Saïd, Soufi, Ahmad El
core   +3 more sources

From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View

, 2013
A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits).
Turbiner, Alexander V.
core   +2 more sources

A review of Hardy inequalities [PDF]

arXiv, 1998
We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.
arxiv