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Cartesian Currents in the Calculus of Variations I (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge   A Series of Modern Surveys in Mathematics)
 
 
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Cartesian Currents in the Calculus of Variations I (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) [Hardcover]

Mariano Giaquinta (Author), Giuseppe Modica (Author), Jiri Soucek (Author)

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Book Description

3540640096 978-3540640097 September 18, 1998 1
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

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"Bei dieser Monographie handelt es sich um einen Bericht von der vordersten Forschungsfront, der gleichzeitig jedem an dieser Art von Problemen interessierten Mathematiker zugänglich ist. Das ist ein seltener Glücksfall, für den man den Autoren gar nicht genug danken kann. Wer sich durch den schieren Umfang der beiden Bände nicht abschrecken lässt, wird diese, einmal zur Hand genommen, nicht so schnell wieder ins Regal zurückstellen wollen. DMV Jahresbericht Bd. 103, Heft 1, 2001

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Inside This Book (learn more)
First Sentence:
This chapter deals with general measure theory. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constancy theorem, integer multiplicity rectifiable currents, rectifiability theorem, distributional determinant, bounded weak convergence, approximate differentiability, homological invariance, slicing theory, polyhedral chain, slicing lemma, boundaryless case, relative cohomology class, approximate tangent plane, deformation theorem, approximate tangent space, flatness theorem, integral homology classes, flat chains, coarea formula, retraction map, real homology, closure theorem, higher integrability, homotopy formula, flat norm
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Homology Induced Maps, Idet Duk
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