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Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under;

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Hamilton's Ricci Flow

Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow;

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Aspects Of Sobolev-Type Inequalities

This book, first published in 2001, focuses on Poincare, Nash and other Sobolev-type inequalities and their applications to the Laplace and;

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Lectures on the Ricci Flow

of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory;

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Sobolev Spaces On Metric Measure Spaces

landmark theorems, including Cheeger's stability theorem for Poincare inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self;

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Nonlinear Potential Theory and Weighted Sobolev Spaces

Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincare inequalities, Maz'ya type;

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Around the Research of Vladimir Maz'ya I

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often;

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Ricci Flow and the Sphere Theorem

manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's;

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Random Walks and Heat Kernels on Graphs

of isoperimetric and Poincare inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these;

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Fractional Differentiation Inequalities

In this book the author presents the Opial, Poincare, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for;

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The Poincare Conjecture

in 2000. Six years later, an eccentric Russian mathematician had the answer. Here, Donal O'Shea explains the maths behind the Conjecture and;

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Inequalities Based on Sobolev Representations

types and of integral means, all of which depend upon the Sobolev integral representations of functions. Applications illustrate inequalities;

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The Ricci Flow: Techniques and Applications: Part III

, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the;

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Analysis and Geometry of Markov Diffusion Operators

such as Poincare, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it;

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Lectures on Nonsmooth Differential Geometry

differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow;

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Lectures on Nonsmooth Differential Geometry

differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow;

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Mean Curvature Flow and Isoperimetric Inequalities

Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface;

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Heat Kernels And Spectral Theory

An advanced monograph on a central topic in the theory of differential equations, Heat Kernels and Spectral Theory investigates the theory;

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Inequalities for Differential Forms

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms;

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The Ricci Flow: Techniques and Applications: Part II

Geometric analysis has become one of the most important tools in geometry and topology. In their books on the Ricci flow, the authors;

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Multi-Valued Variational Inequalities and Inclusions

variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz;

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Multi-Valued Variational Inequalities and Inclusions

variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz;

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Advanced Inequalities

This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the;

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Half-discrete Hilbert-type Inequalities

homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof;

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Theory of Reproducing Kernels and Applications

, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit;

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Geometric Analysis

of geometric evolution, with more detailed lectures on Ricci flow and Kahler-Ricci flow, new progress on the analytic aspects of the Willmore equation;

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Heat Transfer and Fluid Flow in Minichannels and Microchannels

fluxes under single-phase and two-phase applications. Heat Transfer and Fluid Flow in Minichannels and Microchannels methodically covers gas;

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