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Level: BSc, MSci, MSc
Title: Birkhoff's curve shortening process and closed geodesics
Supervisor:

Dr Reto Buzano
Research Area: Geometry and Analysis
Description:

The project is driven by the question whether or not a given closed curve on a closed surface can be "modified" in some way to become a geodesic. This question led to Birkhoff's curve shortening process as well as the curve shortening flow (see also project Curve Shortening Flow in the Plane). The goal of this project is to study Birkhoff's curve shortening process as well as its properties and applications. The project is mainly reading a chapter from the book below and restating/reproving its content. Please contact the supervisor for more details.
Further Reading:
  • T.  H. Colding, W. P. Minicozzi II, A Course in Minimal Surfaces. Graduate Studies in Mathematics, Vol. 121, American Mathematical Society, 2011.

 
Key Modules:

MTH5109 Geometry II: Knots and Surfaces

MTH5104 Convergence and Continuity
Other Information:

The more Geometry and Analysis you have done, the better you are suited for this project.
Current Availability: Yes