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Aspects of Sobolev-Type Inequalities

By (author) Laurent Saloff-Coste

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This book, first published in 2001, focuses on Poincare, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincare and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincare's inequality on the other. It is suitable to be used as an advanced graduate textbook and will also be a useful source of information for graduate students and researchers in analysis on manifolds, geometric differential equations, Brownian motion and diffusion on manifolds, as well as other related areas.

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The Colonialist: The Vision of Cecil Rhodes

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Paperback / softback
528 pages
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This first comprehensive biography of Cecil Rhodes in a generation illuminates Rhodesâ€™s vision for the expansion of imperialism in southern Africa, connecting politics and industry to internal development, and examines how this fueled a lasting, white-dominated colonial society.

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Paperback / softback
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