Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying ""theory of inequalities."" For certain kinds of inequalities, the notion of majorization leads to such…
In this memoir, we study the interrelations between the topological, measure theoretical and geometrical structures in certain classes of Banach spaces. The focus is on those spaces whose bounded subsets have arbitrarily norm-small convex combinations of slices. This class conta…
"The appearance of Grnbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promis…
"The original edition ... inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branch…
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Four…