Projects per year
Abstract
This short chapter is a mostly expository note examining negatively curved three-manifolds. We look at some rigidity properties related to isometric embeddings into Minkowski space. We also review the cross curvature flow (XCF) as a tool to study the space of negatively curved metrics on hyperbolic three-manifolds, the largest and least understood class of model geometries in Thurston’s geometrisation. The relationship between integrability and embeddability yields interesting insights, and we show that solutions with fixed Einstein volume are precisely the integrable solutions, answering a question posed by Chow and Hamilton when they introduced the XCF.
Original language | English |
---|---|
Title of host publication | Differential geometry in the large |
Editors | Owen Dearricott, Wilderich Tuschmann, Yuri Nikolayevsky, Thomas Leistner, Diarmuid Crowley |
Place of Publication | Cambridge, UK ; New York, US ; Victoria, AU ; New Delhi, India |
Publisher | Cambridge University Press (CUP) |
Chapter | 3 |
Pages | 75-97 |
Number of pages | 23 |
ISBN (Electronic) | 9781108884136 |
ISBN (Print) | 9781108812818 |
DOIs | |
Publication status | Published - 2021 |
Event | Australian–GermanWorkshop on Differential Geometry in the Large (2019) - Creswick, Australia Duration: 4 Feb 2019 → 15 Feb 2019 |
Publication series
Name | London Mathematical Society Lecture Note Series |
---|---|
Publisher | Cambridge University Press |
Volume | 463 |
Conference
Conference | Australian–GermanWorkshop on Differential Geometry in the Large (2019) |
---|---|
Country/Territory | Australia |
City | Creswick |
Period | 4/02/19 → 15/02/19 |
Fingerprint
Dive into the research topics of 'Negatively curved three-manifolds, hyperbolic metrics, isometric embeddings in minkowski space and the cross curvature flow'. Together they form a unique fingerprint.Projects
- 1 Finished
-
Analysis of fully non-linear geometric problems and differential equations
3/01/18 → 2/01/21
Project: Research