Differential geometry Surfaces in Euclidean space Concept
Mean curvature
Summary
The mean curvature of a surface at a point is the average of its two principal curvatures. Unlike the Gaussian curvature, it depends on how the surface sits in space, and its sign depends on the choice of unit normal. Surfaces with mean curvature zero are the minimal surfaces, such as soap films, and surfaces of constant mean curvature model soap bubbles.
Where this leads
15 pages build on this one.
- Huisken's theorem on convex hypersurfaces
- Mean curvature flow
- Plateau's laws
- Constant-mean-curvature surface
- Jean Taylor's theorem on soap film singularities
- Willmore energy
- Willmore flow
- Kelvin problem
- Minimal surface
- Simons cone
- Level-set method
- Allard regularity theorem
- Weaire–Phelan structure
- Bombieri–De Giorgi–Giusti theorem
- Inverse mean curvature flow
Further reading
About this page
| Tag | PA78NFEPCF |
|---|---|
| URI | m2://PA78NFEPCF |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A05, 53A10 |
| Same as |
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What links here
Used by
- Huisken's theorem on convex hypersurfaces
- Mean curvature flow
- Plateau's laws
- Constant-mean-curvature surface
- Willmore energy
- Willmore flow
- Minimal surface
- Simons cone
- Level-set method
- Allard regularity theorem
- Inverse mean curvature flow