This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems (not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.
This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems (not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.
Derived from the renowned multi-volume International Encyclopaedia of Laws, this practical analysis of the law of contracts in Italy covers every aspect of the subject - definition and classification of contracts, contractual liability, relation to the law of property, good faith, burden of proof, defects, penalty clauses, arbitration clauses, remedies in case of non-performance, damages, power of attorney, and much more. Lawyers who handle transnational contracts will appreciate the explanation of fundamental differences in terminology, application, and procedure from one legal system to another, as well as the international aspects of contract law. Throughout the book, the treatment emphasizes drafting considerations. An introduction in which contracts are defined and contrasted to torts, quasi-contracts, and property is followed by a discussion of the concepts of ‘consideration’ or ‘cause’ and other underlying principles of the formation of contract. Subsequent chapters cover the doctrines of ‘relative effect’, termination of contract, and remedies for non-performance. The second part of the book, recognizing the need to categorize an agreement as a specific contract in order to determine the rules which apply to it, describes the nature of agency, sale, lease, building contracts, and other types of contract. Facts are presented in such a way that readers who are unfamiliar with specific terms and concepts in varying contexts will fully grasp their meaning and significance. Its succinct yet scholarly nature, as well as the practical quality of the information it provides, make this book a valuable time-saving tool for business and legal professionals alike. Lawyers representing parties with interests in Italy will welcome this very useful guide, and academics and researchers will appreciate its value in the study of comparative contract law.
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