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Hajime Urakawa has written 2 work(s)
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cover image for 9789813109087
Product Description: The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau's estimate of the first eigenvalue, the Lichnerowicz–Obata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and Payne–Pólya–Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described...read more

Hardcover:

9789813109087 | World Scientific Pub Co Inc, November 30, 2016, cover price $98.00 | About this edition: The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum.

cover image for 9780821845813
Product Description: This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods...read more

Hardcover:

9780821845813 | Amer Mathematical Society, November 1, 1993, cover price $105.00 | About this edition: This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science.

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