Nodal sets of eigenfunctions on Riemannian manifolds
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Publication:1112407
DOI10.1007/BF01393691zbMath0659.58047OpenAlexW2043419082MaRDI QIDQ1112407
Harold Donnelly, Charles L. Fefferman
Publication date: 1988
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143593
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
- Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
- Eigenfunctions and nodal sets
- Differential equations on riemannian manifolds and their geometric applications