作者 Bielawski, Roger
書名 Variational Problems in Differential Geometry
出版項 Cambridge : Cambridge University Press, 2011
©2011
國際標準書號 9781139157742 (electronic bk.)
9780521282741
book jacket
說明 1 online resource (218 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 London Mathematical Society Lecture Note Series ; v.394
London Mathematical Society Lecture Note Series
附註 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
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
The state of the art from an internationally respected line up of authors working in geometric variational problems
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Bielawski, Roger Variational Problems in Differential Geometry Cambridge : Cambridge University Press,c2011 9780521282741
主題 Geometry, Differential -- Congresses
Electronic books
Alt Author Houston, Kevin
Speight, Martin