Geometric properties of eigenfunctions
D Jakobson, N Nadirashvili, J Toth - Russian Mathematical …, 2001 - iopscience.iop.org
We give an overview of some new and old results on geometric properties of eigenfunctions
of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical …
of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical …
Local and global analysis of eigenfunctions
S Zelditch - arXiv preprint arXiv:0903.3420, 2009 - arxiv.org
This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly
compact and without boundary). We discuss both local results obtained by analyzing …
compact and without boundary). We discuss both local results obtained by analyzing …
Counting nodal lines which touch the boundary of an analytic domain
JA Toth, S Zelditch - Journal of Differential Geometry, 2009 - projecteuclid.org
We consider the zeros on the boundary∂ Ω of a Neumann eigenfunction ϕλj of a real
analytic plane domain Ω. We prove that the number of its boundary zeros is O (λj) where−∆ …
analytic plane domain Ω. We prove that the number of its boundary zeros is O (λj) where−∆ …
Review of Yau's conjecture on zero sets of Laplace eigenfunctions
A Logunov, E Malinnikova - arXiv preprint arXiv:1908.01639, 2019 - arxiv.org
This is a review of old and new results and methods related to the Yau conjecture on the
zero set of Laplace eigenfunctions. The review accompanies two lectures given at the …
zero set of Laplace eigenfunctions. The review accompanies two lectures given at the …
Eigenfunctions and nodal sets
S Zelditch - arXiv preprint arXiv:1205.2812, 2012 - arxiv.org
arXiv:1205.2812v1 [math.SP] 12 May 2012 Page 1 EIGENFUNCTIONS AND NODAL SETS
STEVE ZELDITCH Abstract. This is a survey of recent results on nodal sets of eigenfunctions …
STEVE ZELDITCH Abstract. This is a survey of recent results on nodal sets of eigenfunctions …
Neumann domains on graphs and manifolds
A Laplacian eigenfunction on a manifold or a metric graph imposes a natural partition of the
manifold or the graph. This partition is determined by the gradient vector field of the …
manifold or the graph. This partition is determined by the gradient vector field of the …
Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution
J Jung, S Zelditch - Journal of Differential Geometry, 2016 - projecteuclid.org
We prove two types of nodal results for density $1 $ subsequences of an orthonormal basis
$\{\phi_j\} $ of eigenfunctions of the Laplacian on a negatively curved compact surface $(M …
$\{\phi_j\} $ of eigenfunctions of the Laplacian on a negatively curved compact surface $(M …
An introduction to the study of critical points of solutions of elliptic and parabolic equations
R Magnanini - arXiv preprint arXiv:1604.00530, 2016 - arxiv.org
We give a survey at an introductory level of old and recent results in the study of critical
points of solutions of elliptic and parabolic partial differential equations. To keep the …
points of solutions of elliptic and parabolic partial differential equations. To keep the …
Eigenfunctions with infinitely many isolated critical points
We construct a Riemannian metric on the 2D torus, such that for infinitely many eigenvalues
of the Laplace–Beltrami operator, a corresponding eigenfunction has infinitely many isolated …
of the Laplace–Beltrami operator, a corresponding eigenfunction has infinitely many isolated …
Eigenfunctions with prescribed nodal sets
A Enciso, D Peralta-Salas - Journal of Differential Geometry, 2015 - projecteuclid.org
In this paper we consider the problem of prescribing the nodal set of low-energy
eigenfunctions of the Laplacian. Our main result is that, given any separating closed …
eigenfunctions of the Laplacian. Our main result is that, given any separating closed …