Zeros of orthogonal polynomials

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The Foundations Of Differential Geometry

We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, can one hear the shape of a drum? In order to construct simply connected examples, we exploit the observation that an orbifold whose underlying space is a simply connected manifold with boundary need not be simply connected as an orbifold

/pdf/one-cannot-hear-the-shape-of-a-drum-44ybua5ji5.pdf

One cannot hear the shape of a drum

Isospectral plane domains and surfaces via Riemannian orbifolds.

http://library.um.ac.id/free-contents/downloadpdf.php/buku/methods-of-modern-mathematical-physics-vol-i-functional-analysis-reed-michael-barry-simon-12066.pdf

Methods of modern mathematical physics (vol.) I : functional analysis / Reed Michael, Barry Simon)

© Séminaire de Théorie spectrale et géométrie (Chambéry-Grenoble), 1990-1991, tous droits réservés. L’accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Transplantation et isospectralité. I

Eigenvalue and “Twisted” eigenvalue problems, applications to CMC surfaces

In this paper, we revisit Courant’s nodal domain theorem for the Dirichlet eigenfunctions of a square membrane, and the analyses of A. Stern and A. Pleijel.

https://hal.archives-ouvertes.fr/hal-00951531/document

Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses

/pdf/transplantation-et-isospectralite-ii-2kihhb58w7.pdf

Transplantation Et Isospectralité II

The main result of this paper states that the traceless second fundamental tensor \({A}^{0}\)of an n-dimensional complete hypersurface M, with constant mean curvature H and finite total curvature, \(\int{M}^{|A^0|^n{d\nu}}{M} 0,\) any such surface must be compact.

Pierre Bérard

Papers

Transplantation et isospectralité. I

Eigenvalue and “Twisted” eigenvalue problems, applications to CMC surfaces

Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses

Transplantation Et Isospectralité II

Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature