On the contact geometry of nodal sets

DOI10.1090/S0002-9947-05-03970-XzbMath1156.53318arXivmath/0402070MaRDI QIDQ3373715

Rafal Komendarczyk

Publication date: 8 March 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402070

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Contact manifolds (general theory) (53D10)

Related Items

Laplace operators with eigenfunctions whose nodal set is a knot ⋮ Nodal sets of Laplace eigenfunctions under small perturbations ⋮ Beltrami vector fields with an icosahedral symmetry ⋮ Contact structures and Beltrami fields on the torus and the sphere ⋮ Morse functions and contact convex surfaces ⋮ Tight Beltrami fields with symmetry ⋮ Dividing sets as nodal sets of an eigenfunction of the Laplacian

Cites Work

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• Generic properties of the eigenvalue of the Laplacian for compact Riemannian manifolds
• On the nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^ 2\)
• Potential and scattering theory on wildly perturbed domains
• Eigenfunctions and nodal sets
• Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains
• On the classification of tight contact structures. I
• Collapsing of connected sums and the eigenvalues of the Laplacian
• On the classification of tight contact structures. II.
• Classification of overtwisted contact structures on 3-manifolds
• Hodge-Laplace operator on compact manifolds deprived of a finite number of balls.
• TIGHT CONTACT STRUCTURES ON LENS SPACES
• Generic Properties of Eigenfunctions
• Closed Nodal Lines and Interior Hot Spots of the Second Eigenfunctions of the Laplacian on Surfaces
• Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture
• Overtwisted energy-minimizing curl eigenfields
• Isoperimetric Inequalities and Their Applications
• Contact structures on manifolds fibered by circles above a surface