Cartesian currents in the calculus of variations, II, variational integrals / Mariano Giaquinta, Giuseppe Modica, Jiri Soucek

... A number of open questions are mentioned in the book, and the sections are followed by very informative discussions of the literature. The size of the monograph also owes to the attempt of the authors "to make each chapter, and sometimes even sections, readable independently of the general context''. The book will definitely be interesting for researchers in the calculus of variations; however, because of its style, and its illustrative, simple examples and detailed proofs, parts of it can be studied already at the beginning graduate level. The theory of the authors provides a systematic and geometrically intuitive approach to geometric variational problems, which has led to a couple of interesting results. The volumes presented are designed to make the ideas accessible to a wider audience. (MSN)