scholarly journals Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription

2013 ◽  
Author(s):  
Y. Canzani ◽  
R. Gover ◽  
D. Jakobson ◽  
R. Ponge ◽  
Keyword(s):  
Conformal Invariants ◽  
Nodal Sets ◽  
Negative Eigenvalues

scholarly journals Conformal invariants from nodal sets. II. Manifolds with boundary

2021 ◽  
Author(s):  
Graham Cox ◽  
Dmitry Jakobson ◽  
Mikhail Karpukhin ◽  
Yannick Sire
Keyword(s):  
Manifolds With Boundary ◽  
Conformal Invariants ◽  
Nodal Sets

scholarly journals Lower Bounds for Nodal Sets of Eigenfunctions

2011 ◽  
Vol 306 (3) ◽  
pp. 777-784 ◽  
Author(s):  
Tobias H. Colding ◽  
William P. Minicozzi
Keyword(s):  
Lower Bounds ◽  
Nodal Sets

Asymptotic eigensolutions of Laplace’s tidal equation

1977 ◽  
Vol 353 (1674) ◽  
pp. 377-400 ◽  
Keyword(s):  
Angular Velocity ◽  
Vertical Structure ◽  
Angular Frequency ◽  
Numerical Results ◽  
Asymptotic Approximations ◽  
Equivalent Depth ◽  
Negative Eigenvalues ◽  
Hough Functions

Asymptotic approximations to the eigenfunctions of Laplace’s tidal equation (Hough functions) are obtained for prescribed λ = σ /2 ω ( σ = angular frequency, ω = angular velocity of planet) and large values of Lamb’s parameter, β = 4 ω 2 a 2 / gh ( a is the planetary radius, and h the equivalent depth for a particular vertical structure), qua eigenvalue. Both positive and negative eigenvalues are considered. The results are validated by comparison with the extensive numerical results of Flattery (1967) and Longuet-Higgins (1968). They should be useful in atmospheric tidal studies, especially for a rapidly rotating planet, and may be useful for studies of equatorial motions in the oceans.

scholarly journals Equidistribution of the conormal cycle of random nodal sets

2018 ◽  
Vol 20 (12) ◽  
pp. 3017-3071
Author(s):  
Nguyen Viet Dang ◽  
Gabriel Rivière
Keyword(s):  
Nodal Sets
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