| EPSRC Reference: |
EP/L003163/1 |
| Title: |
The geometry of a surface embedded in a 3-manifold with constant mean curvature |
| Principal Investigator: |
Tinaglia, Dr G |
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| Department: |
Mathematics |
| Organisation: |
Kings College London |
| Scheme: |
Overseas Travel Grants (OTGS) |
| Starts: |
25 August 2013 |
Ends: |
24 August 2014 |
Value (£): |
13,013
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
While the theory of constant mean curvature surfaces is a purely mathematical one, such surfaces overtly present themselves in nature and are studied in many material sciences. This makes the theory more exciting and adds value to the project. If we take a closed wire and dip it in and out of soapy water, the soap film that forms across the hoop is in fact a minimal (constant mean curvature equal to zero) surface, and the physical properties of soap films were already studied by Plateau in the 1850s. Among all surfaces spanning a given boundary, a soap film is the one with least area. While the air pressure on the sides of a soap film is equal and constant, if we change the pressure on one side, for instance by blowing air on it, the new surface that we obtain is a soap bubble. Mathematically, soap bubbles are constant mean curvature surfaces, and they minimize area under a volume constraint.
This project aims to describe several geometric properties of minimal and constant mean curvature surfaces. Roughly speaking, I intend to prove that constant mean curvature surfaces which satisfy certain weak geometric conditions cannot bend too much. I intend to construct examples to show that the previous results are, in a sense, sharp. Finally, I intend to study the limits of certain sequences of minimal surfaces.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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