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  • 1
    Online Resource
    Online Resource
    Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory (2012)
    Cambridge ; : Cambridge University Press,
    Details
    UID:
    almafu_9959228364402883
    Format: 1 online resource (xix, 454 pages) : , digital, PDF file(s).
    ISBN: 1-316-08980-0 , 1-139-56452-8 , 1-283-57495-0 , 1-139-55098-5 , 9786613887405 , 1-139-10813-1 , 1-139-55594-4 , 1-139-55223-6 , 1-139-54973-1 , 1-139-55469-7
    Series Statement: Cambridge studies in advanced mathematics ; 135
    Content: The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Cover; CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 135; CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS; Title; Copyright; Dedication; Contents; Preface; Notation; PART ONE: Radon measures on Rn; Synopsis; 18.2 The coarea formula on Hn-1-rectifiable sets; 1 Outer measures; 1.1 Examples of outer measures; 1.2 Measurable sets and s-additivity; 1.3 Measure Theory and integration; 2 Borel and Radon measures; 2.1 Borel measures and Carath ́eodory's criterion; 2.2 Borel regular measures; 2.3 Approximation theorems for Borel measures; 2.4 Radon measures. Restriction, support, and push-forward , 3 Hausdorff measures3.1 Hausdorff measures and the notion of dimension; 3.2 H1 and the classical notion of length; 3.3 Hn = Ln and the isodiametric inequality; 4 Radon measures and continuous functions; 4.1 Lusin's theorem and density of continuous functions; 4.2 Riesz's theorem and vector-valued Radon measures; 4.3 Weak-star convergence; 4.4 Weak-star compactness criteria; 4.5 Regularization of Radon measures; 5 Differentiation of Radon measures; 5.1 Besicovitch's covering theorem; 5.2 Lebesgue-Besicovitch differentiation theorem; 5.3 Lebesgue points , 6 Two further applications of differentiation theory6.1 Campanato's criterion; 6.2 Lower dimensional densities of a Radon measure; 7 Lipschitz functions; 7.1 Kirszbraun's theorem; 7.2 Weak gradients; 7.3 Rademacher's theorem; 8 Area formula; 8.1 Area formula for linear functions; 8.2 The role of the singular set J f =0; 8.3 Linearization of Lipschitz immersions; 8.4 Proof of the area formula; 8.5 Area formula with multiplicities; 9 Gauss-Green theorem; 9.1 Area of a graph of codimension one; 9.2 Gauss-Green theorem on open sets with C1-boundary , 9.3 Gauss-Green theorem on open sets with almost C1-boundary10 Rectifiable sets and blow-ups of Radon measures; 10.1 Decomposing rectifiable sets by regular Lipschitz images; 10.2 Approximate tangent spaces to rectifiable sets; 10.3 Blow-ups of Radon measures and rectifiability; 11 Tangential differentiability and the area formula; 11.1 Area formula on surfaces; 11.2 Area formula on rectifiable sets; 11.3 Gauss-Green theorem on surfaces; Notes; PART TWO: Sets of finite perimeter; 12 Sets of finite perimeter and the Direct Method; 12.1 Lower semicontinuity of perimeter , 12.2 Topological boundary and Gauss-Green measure12.3 Regularization and basic set operations; 12.4 Compactness from perimeter bounds; 12.5 Existence of minimizers in geometric variational problems; 12.6 Perimeter bounds on volume; 13 The coarea formula and the approximation theorem; 13.1 The coarea formula; 13.2 Approximation by open sets with smooth boundary; 13.3 The Morse-Sard lemma; 14 The Euclidean isoperimetric problem; 14.1 Steiner inequality; 14.2 Proof of the Euclidean isoperimetric inequality; 15 Reduced boundary and De Giorgi's structure theorem , 15.1 Tangential properties of the reduced boundary , English
    Additional Edition: ISBN 1-107-47172-9
    Additional Edition: ISBN 1-107-02103-0
    Language: English
    URL: Volltext
    URL: Inhaltstext
    URL: https://doi.org/10.1017/CBO9781139108133
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    FU Berlin
    UB Potsdam
  • 2
    Book
    Book
    Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory (2012)
    Cambridge [u.a.] : Cambridge Univ. Press
    Details
    UID:
    b3kat_BV040299221
    Format: XIX, 454 Seiten , Diagramme
    ISBN: 9781107021037
    Series Statement: Cambridge studies in advanced mathematics 135
    Language: English
    Subjects: Mathematics
    RVK:
    SK 430
    RVK:
    SK 660
    Keywords: Geometrische Maßtheorie ; Variationsproblem
    URL: Cover image
    URL: Contributor biographical information
    URL: Publisher description
    URL: Table of contents only
    URL: Inhaltsverzeichnis
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  • 3
    Book
    Book
    Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory (2012)
    Cambridge [u.a.] :Cambridge Univ. Press,
    Details
    UID:
    almahu_BV040299221
    Format: XIX, 454 Seiten : , Diagramme.
    ISBN: 978-1-107-02103-7
    Series Statement: Cambridge studies in advanced mathematics 135
    Language: English
    Subjects: Mathematics
    RVK:
    SK 430
    RVK:
    SK 660
    Keywords: Geometrische Maßtheorie ; Variationsproblem
    URL: Cover image
    URL: Contributor biographical information
    URL: Publisher description
    URL: Table of contents only
    URL: Inhaltsverzeichnis
    URL: Cover image
    URL: Contributor biographical information
    URL: Publisher description
    URL: Table of contents only
    URL: Inhaltsverzeichnis
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Book
    HU Berlin get availability status
    FU Berlin get availability status
  • 4
    Book
    Book
    Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory (2012)
    Cambridge [u. a.] : Cambridge Univ. Press
    Details
    UID:
    gbv_718254376
    Format: XIX, 454 S. , Ill., graph. Darst. , 24 cm
    Edition: First published
    ISBN: 9781107021037
    Series Statement: Cambridge studies in advanced mathematics 135
    Content: "The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory"--
    Note: Includes bibliographical references (p. [445]-452) and index , Machine generated contents note: 1. Radon measures on Rn; 2. Sets of finite perimeter; 3. Regularity theory and analysis of singularities; 4. Minimizing clusters.
    Additional Edition: Online-Ausg. (MyiLibrary) Maggi, Francesco, 1978 - Sets of finite perimeter and geometric variational problems New York : Cambridge University Press, 2012 ISBN 9781283574952
    Additional Edition: ISBN 1283574950
    Additional Edition: ISBN 9781139550987
    Additional Edition: Erscheint auch als Online-Ausgabe Maggi, Francesco, 1978 - Sets of finite perimeter and geometric variational problems Cambridge : Cambridge University Press, 2012 ISBN 9781107021037
    Additional Edition: ISBN 9781107471726
    Additional Edition: ISBN 9781139108133
    Additional Edition: Online-Ausg. (Ebrary) Maggi, Francesco, 1978 - Sets of finite perimeter and geometric variational problems Cambridge [u.a.] : Cambridge University Press, 2012 ISBN 9781107021037
    Language: English
    Subjects: Mathematics
    RVK:
    SK 430
    Keywords: Geometrische Maßtheorie ; Variationsproblem
    URL: Inhaltsverzeichnis
    URL: Cover
    URL: Autorenbiografie
    URL: Verlagsangaben
    URL: Inhaltstext
    Library Location Call Number Volume/Issue/Year Availability
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    Book
    UB Potsdam get availability status
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