Differential geometry in the large / edited by Owen Dearricott, Wilderich Tuschmann, Yuri Nikolayevsky, Thomas Leistner, Diarmuid Crowley.

Format:

Book

Contributor:

Dearricott, Owen, editor.

Tuschmann, Wilderich, 1967- editor.

Nikolayevsky, Yuri (Mathematician), editor.

Leistner, Thomas, editor.

Crowley, Diarmuid, editor.

Series:

London Mathematical Society lecture note series ; 463.

London Mathematical Society lecture note series ; 463

Language:

English

Subjects (All):

Geometry, Differential.

Physical Description:

xvi, 384 pages : illustrations ; 23 cm.

Place of Publication:

Cambridge, United Kingdom : Cambridge University Press, 2021.

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.

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

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

Notes:

Includes bibliographical references.

ISBN:

9781108812818

1108812813

OCLC:

1227054424