Riemannian manifolds admitting isometric immersions by their first eigenfunctions

By Ahmad El Soufi, S. Ilias. 2000

103 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/53bd6452f1b74ee3d94c62659bfcece3fc1dcc9b

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In Applied Mathematics

In Astronomy and Astrophysics

In Mathematical Physics

Citations in the corpus

Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold (2007, methodology): “The proof of “(i) implies (ii)” uses arguments similar to those used in the case of closed manifolds by Nadirashvili [25] and the authors [12].”
Extremal Eigenvalues of the Laplacian in a Conformal Class of Metrics: The `Conformal Spectrum' (2003, background): “In [EI3] (see also [ EI4 ] and [N]), Ilias and the second author studied the property for a Riemannian metric to be critical (in a generalized sense) for the functional g 7−→ �k(g).”
SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “This characterization is similar to that of extremizers of the eigenvalues of the Laplace operator on surfaces (see [85, 31, 32]).”
A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle (2006, unknown): “Λ(K) = λ1(K, g0)A(K, g0) = 12πE(2 √ 2/3) ≃ 13.365π, where E(2 √ 2/3) is the complete elliptic integral of the second kind evaluated at 2 √ 2 3 .”
Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces (2013, background): “[14] A. El Soufi and S. Ilias.”
An isoperimetric inequality for Laplace eigenvalues on the sphere (2017, unknown): “More results on extremal metrics on tori and Klein bottles could be found in the papers [18, 27, 28, 29, 34, 47, 48, 50].”
Laplacian eigenvalue functionals and metric deformations on compact manifolds (2007, background): “M G ] 2 6 Ja n 20 07”