The subject matter of this book is fundamental to all areas of mathematical analysis and should be accessible to students who are in the early stages of their professional training. An undergraduate course in real variables is a prerequisite, and an acquaintance with complex analysis is desirable. However, since no use is made of the Cauchy theory, the exposure to complex variables need not be extensive. To fully appreciate Chapters 3 and 4 some background in elementary point-set topology is essential.
If you have ever eaten food at a restaurant, had someone cook for you, or cooked something yourself, you have seen math in action. How Chefs Use Math demonstrateshow chefs use math to measure, prepare, and cook to create tasty, delicious food.
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This work is intended to give a quick overview on the subject of the geometric measure theory with emphases on various basic ideas, techniques and their applications in problems arising in the calculus of variations, geometrical analysis and nonlinear partial differential equations.
Functional Inequalities Markov Semigroups and Spectral Theory
In this book, the functional inequalities are introduced to describe: (i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap; (ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density; (iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.
