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Title Differential geometry in the large / edited by Owen Dearricott, Wilderich, Tuschmann, Yuri Nikolayevsky, Thomas Leistner, [and] Diarmuid Crowley
Published Cambridge, United Kingdom : Cambridge University Press, 2020
©2020

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Description 1 online resource (xvi, 384 pages)
Series London Mathematical Society Lecture note series ; 463
London Mathematical Society lecture note series ; 463.
Contents Cover -- Series information -- Title page -- Copyright information -- Epigraph -- Contents -- List of contributors -- Introduction -- Part One Geometric Evolution Equations and Curvature Flow -- 1 Real Geometric Invariant Theory -- 1.1 Introduction -- 1.2 Examples -- 1.3 Comparison with Complex and Symplectic Case -- 1.4 The Abelian Case -- 1.5 Separation of Closed T-Invariant Sets -- 1.6 The General Case of Real Reductive Groups -- 1.7 Stratification -- 1.8 Properties of Critical Points of the Energy Map -- 1.9 Applications -- 1.10 Appendices -- 1.10.1 Real Reductive Lie Groups
1.10.2 The Parabolic Subgroup Q[sub(ß)] -- References -- 2 Convex Ancient Solutions to Mean Curvature Flow -- 2.1 Introduction -- 2.2 Asymptotics for Convex Ancient Solutions -- 2.3 X.-J. Wang's Dichotomy for Convex Ancient Solutions -- 2.4 Convex Ancient Solutions to Curve Shortening Flow -- 2.5 Rigidity of the Shrinking Sphere -- 2.6 Asymptotics for Convex Translators -- 2.7 X.-J. Wang's Dichotomy for Convex Translators -- 2.8 Rigidity of the Bowl Soliton -- References
3 Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings in Minkowski Space and the Cross Curvature Flow -- 3.1 Introduction -- 3.2 Geometrisation of Three-Manifolds -- 3.3 Embeddability and Hyperbolic Metrics -- 3.4 The Cross Curvature Flow -- 3.4.1 Definition and Basic Properties of the Flow -- 3.4.2 Short Time Existence and Uniqueness -- 3.4.3 Basic Identities and Evolution Equations -- 3.4.4 Towards Hyperbolic Convergence -- 3.4.5 Harnack Inequality and Solitons -- 3.4.6 Monotonicity of Einstein Volume -- References
4 A Mean Curvature Flow for Conformally Compact Manifolds -- 4.1 Introduction -- 4.2 Conformal Geometry and Hypersurfaces in Conformally Compact Manifolds -- 4.2.1 Conformal Manifolds -- 4.2.2 The Tractor Connection -- 4.2.3 Conformally Compact Manifolds -- 4.2.4 Hypersurfaces -- 4.2.5 A Hypersurface Flow for Conformally Compact Manifolds -- 4.2.6 Boundary Conditions -- 4.2.7 The Flow Problem -- 4.3 The Flow Problem -- 4.3.1 Treating the Flow as a Nonlinear Partial Differential Equation -- 4.3.2 Generalised Mean Curvature Flow in Hyperbolic Space -- 4.3.3 Long Time Existence and Convergence
Summary "The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry"--Provided by publisher
Bibliography Includes bibliographical references
Notes Online resource; title from digital title page (viewed on October 21, 2020)
Subject Geometry, Differential.
Mathematical recreations.
Geometry.
Topology.
geometry.
Topología
Geometry
Geometry, Differential
Mathematical recreations
Topology
Form Electronic book
Author Dearricott, Owen, editor.
Tuschmann, Wilderich, 1967- editor.
Nikolayevsky, Yuri, editor
Leistner, Thomas, editor
Crowley, Diarmuid, editor
ISBN 1108879993
9781108884136
110888413X
9781108879996