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050  4 QA641 .V37 2012 
082 0  516.36 
100 1  Bielawski, Roger 
245 10 Variational Problems in Differential Geometry 
264  1 Cambridge :|bCambridge University Press,|c2011 
264  4 |c©2011 
300    1 online resource (218 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  London Mathematical Society Lecture Note Series ;|vv.394 
505 0  Cover -- LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES -
       - Conference photograph -- Title -- Copyright -- Contents 
       -- Contributors -- Preface -- Chapter 1 The supremum of 
       first eigenvalues of conformally covariant operators in a 
       conformal class -- Abstract -- 1.1 Introduction -- 1.2 
       Preliminaries -- 1.2.1 Notations -- 1.2.2 Removal of 
       singularities -- 1.2.3 Conformally covariant elliptic 
       operators -- 1.2.4 Invertibility on Sn-1 × R -- 1.2.5 
       Examples -- 1.3 Asymptotically cylindrical blowups -- 
       1.3.1 Convention -- 1.3.2 Definition of the metrics -- 
       1.3.3 Eigenvalues and basic properties on (M,gL) -- 1.3.4 
       Analytical facts about (M∞, g∞) -- 1.3.5 The kernel -- 
       1.4 Proof of the main theorem -- 1.4.1 Stronger version of
       the main theorem -- 1.4.2 The supremum part of the proof 
       of Theorem 1.4.1 -- 1.4.3 The infimum part of the proof of
       Theorem 1.4.1 -- Appendix A Analysis on (M∞, g∞) -- 
       References -- Chapter 2 K-Destabilizing test 
       configurations with smooth central fiber -- Abstract -- 
       2.1 Introduction -- 2.2 The case of normal singularities -
       - 2.3 Proof of Theorem 2.1.8 and examples -- References --
       Chapter 3 Explicit constructions of Ricci solitons -- 
       Abstract -- 3.1 Introduction -- 3.2 Solitons from a 
       dynamical system -- 3.3 Reduction of the equations to a 2-
       dimensional system -- 3.4 Higher dimensional Ricci 
       solitons via projection -- 3.5 The 4-dimensional geometry 
       Nil4 -- References -- Chapter 4 Open Iwasawa cells and 
       applications to surface theory -- 4.1 Introduction -- 4.2 
       Basic notation and the Birkhoff decomposition -- 4.3 
       Iwasawa decomposition -- 4.4 Iwasawa decomposition via 
       Birkhoff decomposition -- 4.5 A function defining the open
       Iwasawa cells -- 4.6 Applications to surface theory -- 
       References -- Chapter 5 Multiplier ideal sheaves and 
       geometric problems -- Abstract -- 5.1 Introduction -- 5.2 
       An overview of multiplier ideal sheaves 
505 8  5.3 Direct relationships between multiplier ideal sheaves 
       and the obstruction F -- References -- Chapter 6 
       Multisymplectic formalism and the covariant phase space --
       6.1 The multisymplectic formalism -- 6.1.1 Maps between 
       vector spaces -- 6.1.2 Higher order problems -- 6.1.3 More
       general multisymplectic manifolds -- 6.1.4 
       Premultisymplectic manifolds -- 6.1.5 Action principle -- 
       6.1.6 Observable functionals -- 6.1.7 Hamilton-Jacobi 
       equations -- 6.1.8 Some historical remarks -- 6.1.9 An 
       example -- 6.2 The covariant phase space -- 6.2.1 A short 
       historical review -- 6.2.2 The basic principle -- 6.2.3 A 
       geometric view of the proof -- 6.3 Geometric quantization 
       -- References -- Chapter 7 Nonnegative curvature on disk 
       bundles -- 7.1 Introduction -- 7.2 Normal homogeneous 
       metrics and Cheeger deformations -- 7.3 Homogeneous 
       metrics of nonnegative curvature -- 7.4 Collar metrics of 
       nonnegative curvature -- 7.5 Bundles with normal 
       homogeneous collar -- 7.6 Cohomogeneity one manifolds -- 
       References -- Chapter 8 Morse theory and stable pairs -- 
       Abstract -- 8.1 Introduction -- 8.2 Stable pairs -- 8.2.1 
       The Harder-Narasimhan stratification -- 8.2.2 Deformation 
       theory -- 8.3 Morse theory -- 8.3.1 The τ-vortex equations
       -- 8.3.2 The gradient flow -- 8.3.3 Negative normal spaces
       -- 8.3.4 Cohomology of the negative normal spaces -- 8.3.5
       The Morse-Bott lemma -- 8.3.6 Perfection of the 
       stratification for large degree -- 8.3.7 The case of low 
       degree -- 8.4 Cohomology of moduli spaces -- 8.4.1 
       Equivariant cohomology of τ -semistable pairs -- 8.4.2 
       Comparison with the results of Thaddeus -- References -- 
       Chapter 9 Manifolds with k-positive Ricci curvature -- 9.1
       Introduction -- 9.2 Manifolds with k-positive Ricci 
       curvature -- 9.3 Fill radius and an approach to Conjecture
       1 -- 9.4 The fundamental group and fill radius bounds -- 
       References 
520    The state of the art from an internationally respected 
       line up of authors working in geometric variational 
       problems 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Geometry, Differential -- Congresses 
655  4 Electronic books 
700 1  Houston, Kevin 
700 1  Speight, Martin 
776 08 |iPrint version:|aBielawski, Roger|tVariational Problems 
       in Differential Geometry|dCambridge : Cambridge University
       Press,c2011|z9780521282741 
830  0 London Mathematical Society Lecture Note Series 
856 40 |uhttps://ebookcentral.proquest.com/lib/sinciatw/
       detail.action?docID=807144|zClick to View