Geometric flows and the geometry of space-time. ([2018])

• Record Type: Book
• Further Information: Note: Vicente Cortés, Klaus Kröncke, Jan Louis, editors.
• Editors: Cortés, Vicente, 1965-; Kröncke, Klaus; Louis, Jan
• Contents: Intro; Preface; Contents; Lorentzian Geometry: Holonomy, Spinors, and Cauchy Problems; Contents; 1 Introduction; 2 Basic Notions; 3 Lorentzian Holonomy Groups; 3.1 Basics on Holonomy Groups; 3.2 Holonomy Groups of Lorentzian Manifolds; 4 Lorentzian Spin Geometry: Curvature and Holonomy; 4.1 Spin Structures and Spinor Fields; 4.2 Curvature and Holonomy of Lorentzian Manifolds with Parallel Spinors; 5 Constraint Equations for Special Lorentzian Holonomy; 5.1 Constraint Equations for Recurrent and Parallel Vector Fields; 5.2 Constraint Equations for Parallel Spinor Fields 6 The Cauchy Problem for the Vacuum Einstein Equations6.1 The Constraint Conditions for the Vacuum Einstein Equations; 6.2 Results from PDE Theory; 6.3 The Vacuum Einstein Equations as Evolution Equations; 6.4 The Vacuum Einstein Equations as Symmetric Hyperbolic System; 7 Cauchy Problems for Lorentzian Special Holonomy; 7.1 Evolution Equations for a Parallel Lightlike Vector Field in the Analytic Setting; 7.2 The Cauchy Problem for a Parallel Lightlike Vector Field as a Symmetric Hyperbolic System; 7.3 Cauchy Problem for Parallel Lightlike Spinors; 8 Geometric Applications 8.1 Applications to Lorentzian Holonomy8.2 Applications to Spinor Field Equations; References; Geometric Flow Equations; Contents; 1 Overview and Plan for the Summer School; 1.1 Plan for the Summer School; 2 Differential Geometry of Submanifolds; 2.1 Graphical Submanifolds; 3 Evolving Submanifolds; 3.1 General Assumption; 3.2 Evolution of Graphs; 3.3 Examples; 3.4 Short-Time Existence and Avoidance Principle; 4 Evolution Equations for Submanifolds; 5 Convex Hypersurfaces; 5.1 Mean Curvature Flow; 5.2 Gauß Curvature Flow and Other Normal Velocities; 5.3 The Tensor Maximum Principle 5.4 Two Dimensional Surfaces5.5 Calculations on a Computer Algebra System; 6 Mean Curvature Flow of Entire Graphs; 7 Mean Curvature Flow Without Singularities; 7.1 Intuition; 7.2 Results; 7.3 Strategy of Proof; 7.4 The A Priori Estimates; Appendix 1: Parabolic Maximum Principles; Appendix 2: Some Linear Algebra; References
• Publisher Details: Cham, Switzerlad : Birkhauser
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 516; Geometry; Space and time; Geometry; Space and time; Electronic books
• Languages: English
• ISBNs: 9783030011260; 3030011267
• Related ISBNs: 9783030011253
• Notes: Note: Description based on online resource; title from digital title page (viewed on January 23, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.