Cartesian Currents in the Calculus of Variations I

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

• geometric measure theory
• harmonic mappings
• minimal surfgaces
• nonlinear elasticity
• weakly differentiable maps

• Scuola Normale Superiore Dipartimento di Matematica, Pisa, Italy

  Mariano Giaquinta

• Dipartimento di Sistemi e Informatica, Università Firenze, Firenze, Italy

  Giuseppe Modica

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