Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Minimal surface
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
{{Short description|Surface that locally minimizes its area}} {{Distinguish|text= [[minimal rational surface]] or [[Enriques–Kodaira classification#Minimal models and blowing up|minimal algebraic surface]]}} [[Image:Bulle de savon hélicoïde.PNG|thumb|180px|right|A [[helicoid]] minimal surface formed by a soap film on a helical frame]] In [[mathematics]], a '''minimal surface''' is a surface that locally minimizes its area. This is equivalent to having zero [[mean curvature]] (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a [[soap film]], which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may [[Immersed submanifold#Immersed submanifolds|self-intersect]] or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see [[minimal surface of revolution]]): the standard definitions only relate to a [[local optimum]], not a [[global optimum]].
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)