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.
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About this page
| Tag | PA78NFEPCF |
|---|---|
| URI | m2://PA78NFEPCF |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A05, 53A10 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Huisken's theorem on convex hypersurfaces
- Constant-mean-curvature surface
- Willmore energy
- Willmore flow
- Minimal surface
- Inverse mean curvature flow