Differential geometry Minimal and constant mean curvature surfaces Concept
Minimal surface
Summary
A minimal surface is a surface in space whose mean curvature is zero at every point. Equivalently, small pieces of it are critical points of area: no small deformation that fixes the boundary changes the area to first order. Soap films spanning a wire frame are physical models of minimal surfaces. The subject links differential geometry with complex analysis, the calculus of variations and partial differential equations.
Where this leads
14 pages build on this one.
- Plateau's laws
- Minimal surface equation
- Almgren–Pitts min-max theory
- Jean Taylor's theorem on soap film singularities
- Kelvin problem
- Plateau's problem
- Simons cone
- Douglas–Radó solution of Plateau's problem
- Bernstein's problem
- Riemannian Penrose inequality
- Yau's conjecture on infinitely many minimal surfaces
- Weaire–Phelan structure
- Bombieri–De Giorgi–Giusti theorem
- Weierstrass–Enneper parameterization
Further reading
About this page
| Tag | 41X0YW2R9N |
|---|---|
| URI | m2://41X0YW2R9N |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A10, 49Q05 |
| Specializes | Constant-mean-curvature surface |
| Same as |
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What links here
Results about this
- Plateau's laws
- Minimal surface of revolution
- Plateau's problem
- Yau's conjecture on infinitely many minimal surfaces
- Weierstrass–Enneper parameterization
Used by
- Plateau's laws
- Minimal surface equation
- Almgren–Pitts min-max theory
- Plateau's problem
- Simons cone
- Douglas–Radó solution of Plateau's problem
- Bernstein's problem
- Riemannian Penrose inequality
- Yau's conjecture on infinitely many minimal surfaces
- Bombieri–De Giorgi–Giusti theorem
- Weierstrass–Enneper parameterization