Displaying similar documents to “Fractals and the base eigenvalue of the Laplacian on certain noncompact surfaces.”

Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals

Pedro Freitas, Batłomiej Siudeja (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Pólya and Szegö's [  (1951)] lower bound for quadrilaterals and extend Hersch's [  (1966) 457–460] upper bound for parallelograms to general quadrilaterals.

Isospectral Riemann surfaces

Peter Buser (1986)

Annales de l'institut Fourier

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We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus g = 5 and for all g 7 . In a second part we give examples of isospectral non isometric surfaces in R 3 which are realizable by paper models.