Ratios of harmonic functions with the same zero set
From MaRDI portal
Publication:311147
DOI10.1007/s00039-016-0369-4zbMath1353.31002arXiv1506.08041OpenAlexW3105834265MaRDI QIDQ311147
Eugenia Malinnikova, Alexander Logunov
Publication date: 29 September 2016
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.08041
Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)
Related Items
Harmonic functions vanishing on a cone ⋮ Factorization of special harmonic polynomials of three variables ⋮ On the nodal set of solutions to degenerate or singular elliptic equations with an application to \(s\)-harmonic functions ⋮ Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in ℝ² ⋮ The nodal set of solutions to anomalous equations ⋮ Improved quantitative unique continuation for complex-valued drift equations in the plane ⋮ Boundary Harnack principle on nodal domains ⋮ Almost-sure asymptotics for Riemannian random waves ⋮ Completely reducible factors of harmonic polynomials of three variables
Cites Work
- Unnamed Item
- Unnamed Item
- A gradient estimate for harmonic functions sharing the same zeros
- On the nodal sets of toral eigenfunctions
- Ruled nodal surfaces of Laplace eigenfunctions and injectivity sets for the spherical mean Radon transform in \(\mathbb{R}^3\)
- Metric properties of eigenfunctions of the Laplace operator on manifolds
- Analytic functions sharing level curves and tracts
- On ratios of harmonic functions
- Nodal sets of harmonic functions
- The variation of the sign of \(V\) for an analytic function \(U+iV\)
- A Characterization of Harmonic Polynomials in the Plane
- Harmonic functions with bounded number of nodal domains
- Sign and area in nodal geometry of Laplace eigenfunctions
- Sur le problème de la division