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Level: BSc, MSci, MSc
Title: Surfaces with critical curvature bounds
Supervisor:

Dr Hug Nguyen
Research Area: Geometry and Analysis
Description:

Surfaces are 2-dimensional objects that play a fundamental role in differential geometry and its applications. When surfaces are immersed in an ambient space they have a natural associated energy called the Willmore energy (or the elastic bending energy). The projects offered here will investigate surfaces with bounds on this critical energy. In particular, we will study optimal co-ordinate systems and their possible degeneration due to concentration phenomena. We will also study various aspects pf the variational problem associated to the elastic bending energy whose critical points are Willmore surfaces.
Further Reading:

Literature suggestions will be supplied.
Key Modules:

MTH5109 Geometry II: Knots and Surfaces

MTH5104 Convergence and Continuity

MTH5105 Differential and Integral Analysis

Other Information:
Current Availability: Yes