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Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Geometric Measure Theory: A Beginner's Guide is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject. New to this edition: New topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjectureNew topical coverage of Manifolds taking account of all recent research advancesThe 2nd edition is comprehensively reworked into two parts, basic theory and applications Focus on core geometry rather than proofs paves the way to fast and efficient insight into an extremely complex topic in geometric structures, enabling further study of more advanced topics and texts. Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniquesFull topical coverage of The Log-Convex Density ConjectureComprehensively updated throughout
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