Nodal Sets for Eigenfunctions of the Laplacian On Surfaces
From MaRDI portal
Publication:3480973
DOI10.2307/1990956zbMath0702.58077OpenAlexW4236414382WikidataQ125848794 ScholiaQ125848794MaRDI QIDQ3480973
Harold Donnelly, Charles L. Fefferman
Publication date: 1990
Full work available at URL: https://doi.org/10.2307/1990956
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)
Related Items (39)
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems ⋮ Equidistribution of the conormal cycle of random nodal sets ⋮ The local structure of nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds ⋮ Stationary sets for the wave equation in crystallographic domains ⋮ Sharp exponential decay for solutions of the stationary perturbed Dirac equation ⋮ Nodal volumes for eigenfunctions of analytic regular elliptic problems ⋮ Critical points of solutions to a kind of linear elliptic equations in multiply connected domains ⋮ On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions ⋮ Critical partitions and nodal deficiency of billiard eigenfunctions ⋮ Asymptotic behavior of the steady Navier-Stokes flow in the exterior domain ⋮ Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions ⋮ Applications of small-scale quantum ergodicity in nodal sets ⋮ Measure upper bounds for nodal sets of eigenfunctions of the bi‐harmonic operator ⋮ Upper bound of critical sets of solutions of elliptic equations in the plane ⋮ Boundary doubling inequality and nodal sets of Robin and Neumann eigenfunctions ⋮ Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure ⋮ Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture ⋮ Bounding the number of nodal domains of eigenfunctions without singular points on the square ⋮ \(L^{p}\) norms, nodal sets, and quantum ergodicity ⋮ Geometry and interior nodal sets of Steklov eigenfunctions ⋮ A Faber-Krahn inequality for solutions of Schrödinger's equation ⋮ Nodal Sets of Laplace Eigenfunctions: Estimates of the Hausdorff Measure in Dimensions Two and Three ⋮ Strong unique continuation for higher order elliptic equations with Gevrey coefficients ⋮ Doubling inequality and nodal sets for solutions of bi-Laplace equations ⋮ On Hörmander's solution of the \(\bar{\partial}\)-equation. I ⋮ Nodal domains and growth of harmonic functions on noncompact manifolds ⋮ A spectral approach to the shortest path problem ⋮ Schauder estimates for elliptic operators with applications to nodal sets. ⋮ A metric Sturm-Liouville theory in two dimensions ⋮ Topological properties of eigenfunctions of Riemannian surfaces ⋮ Quantitative unique continuation for a parabolic equation ⋮ Local weak limits of Laplace eigenfunctions ⋮ Indeterminacy estimates and the size of nodal sets in singular spaces ⋮ Critical sets of solutions to elliptic equations. ⋮ Courant-sharp Robin eigenvalues for the square and other planar domains ⋮ Polynomial upper bound on interior Steklov nodal sets ⋮ Geometry of stationary sets for the wave equation in \(\mathbb R^n\): the case of finitely supported initial data ⋮ On quantitative uniqueness for parabolic equations ⋮ On the Betti numbers of level sets of solutions to elliptic equations
Cites Work
- Nodal sets for solutions of elliptic equations
- A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
- Harmonic maps between surfaces (with a special chapter on conformal mappings)
- Nodal sets of eigenfunctions on Riemannian manifolds
- Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators
- On the length of the nodal curve of an eigenfunction of the Laplace operator
- Finiteness Theorems for Riemannian Manifolds
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Nodal Sets for Eigenfunctions of the Laplacian On Surfaces
