{"product_id":"spectral-geometry-of-the-laplacian-spectral-analysis-and-differential-geometry-of-the-laplacian-hardcover","title":"Spectral Geometry of the Laplacian: Spectral Analysis and Differential Geometry of the Laplacian - Hardcover","description":"\u003cp\u003eby \u003cb\u003eHajime Urakawa\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe 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 \u003cem\u003ek\u003c\/em\u003eth eigenvalues, and Payne-Pólya-Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described. Then, the theorem of Colin de Verdière, that is, the spectrum determines the totality of all the lengths of closed geodesics is described. We give the V Guillemin and D Kazhdan's theorem which determines the Riemannian manifold of negative curvature.\u003c\/p\u003e\u003ch3\u003eFront Jacket\u003c\/h3\u003e\u003cp\u003eThe 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 LichnerowiczObata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and PaynePolyaWeinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described. Then, the theorem of Colin de Verdier, that is, the spectrum determines the totality of all the lengths of closed geodesics is described. We give the V Guillemin and D Kazhdan's theorem which determines the Riemannian manifold of negative curvature.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 312\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.9 x 9.1 x 5.9 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e June 02, 2017\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51793355211040,"sku":"9789813109087","price":191.16,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/b867d6493aa5f44a7cedf4ae43767e96.webp?v=1780719403","url":"https:\/\/ebocreations.com\/products\/spectral-geometry-of-the-laplacian-spectral-analysis-and-differential-geometry-of-the-laplacian-hardcover","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}