Cartesian Currents in the Calculus of Variations II

"Cartesian Currents in the Calculus of Variations II" is a specialized book that addresses non-scalar variational problems significant in various disciplines. It discusses fundamental questions in geometry, such as harmonic mappings between Riemannian manifolds and minimal immersions. Additionally, it covers applications in physics, particularly in the classical theory of a-models, as well as in nonlinear elasticity and the Oseen-Frank theory of liquid crystals. The book provides a comprehensive analysis of the challenges associated with finding energy-minimizing representatives in homology or homotopy classes, highlighting the importance of singularities in vector minimizers. The authors, Mariano Giaquinta, Giuseppe Modica, and Jiri Soucek, present the developments and growing understanding of the general theory of geometric variational problems that have gained significance in recent decades. The discussion on weak formulations and their relevance to the addressed problems is also thoroughly explored.