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New extremal properties for constructing conformal mappings

โœ Scribed by Gerhard Opfer


Publisher
Springer-Verlag
Year
1979
Tongue
English
Weight
282 KB
Volume
32
Category
Article
ISSN
0029-599X

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Extremals for Eigenvalues of Laplacians
โœ Richard Snyder Laugesen; Carlo Morpurgo ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 441 KB

Po lya and G. Szego showed in 1951 that for simply connected plane domains, the first eigenvalue of the Laplacian (with Dirichlet boundary conditions) is maximal for a disk, under a conformal mapping normalization. That is, if f (z) is a conformal map of a disk D onto a bounded, simply connected pla