We prove lower bounds for the length of the zero set of an eigenfunction of the Laplace operator on a Riemann surface; in particular, in non-negative curvature, or when the associated eigenvalue is large, we give a lower bound which involves only the square root of the eigenvalue and the area of the manifold (modulo a numerical constant, this lower bound is sharp)
International audienceFor the spherical Laplacian on the sphere and for the Dirichlet Laplacian in t...
International audienceFor the spherical Laplacian on the sphere and for the Dirichlet Laplacian in t...
AbstractSuppose that φ is an eigenfunction of −Δ with eigenvalue λ≠0. It is proved that ‖φ‖∞⩽c1λn−14...
This is a survey, without proofs, of the main results in [S]. We refer the reader to that paper for ...
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analyti...
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analyti...
Abstract. We prove sharp upper and lower bounds for the nodal length of Steklov eigen-functions on r...
Abstract. We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin in [NPS], that exh...
summary:Let $M$ be an $n$-dimensional ($n\ge 2$) simply connected Hadamard manifold. If the radial R...
Let Ω be a bounded convex domain in R2. Let λ be the lowest eigenvalue of the Laplacian on Ω with Di...
We consider a Laplace eigenfunction φλ on a smooth closed Riemannian manifold, that is, satisfying −...
Abstract. In this paper, we prove that the length of the nodal line of the eigenfunctions associated...
We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds M of finite vo...
We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian...
In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the se...
International audienceFor the spherical Laplacian on the sphere and for the Dirichlet Laplacian in t...
International audienceFor the spherical Laplacian on the sphere and for the Dirichlet Laplacian in t...
AbstractSuppose that φ is an eigenfunction of −Δ with eigenvalue λ≠0. It is proved that ‖φ‖∞⩽c1λn−14...
This is a survey, without proofs, of the main results in [S]. We refer the reader to that paper for ...
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analyti...
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analyti...
Abstract. We prove sharp upper and lower bounds for the nodal length of Steklov eigen-functions on r...
Abstract. We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin in [NPS], that exh...
summary:Let $M$ be an $n$-dimensional ($n\ge 2$) simply connected Hadamard manifold. If the radial R...
Let Ω be a bounded convex domain in R2. Let λ be the lowest eigenvalue of the Laplacian on Ω with Di...
We consider a Laplace eigenfunction φλ on a smooth closed Riemannian manifold, that is, satisfying −...
Abstract. In this paper, we prove that the length of the nodal line of the eigenfunctions associated...
We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds M of finite vo...
We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian...
In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the se...
International audienceFor the spherical Laplacian on the sphere and for the Dirichlet Laplacian in t...
International audienceFor the spherical Laplacian on the sphere and for the Dirichlet Laplacian in t...
AbstractSuppose that φ is an eigenfunction of −Δ with eigenvalue λ≠0. It is proved that ‖φ‖∞⩽c1λn−14...
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