# extremal

An extremum point (i.e. a maximum point or a minimum point) gives a maximum value or a minimum value for a function (http://planetmath.org/RealFunction).

An *extremal curve* (i.e. an *extremal*, or the corresponding *extremal function*) gives a maximum value or a minimum value for a functional^{} (http://planetmath.org/Functional).

For example, if the functional is the length of a curve connecting two points on a sphere, the extremals are great circle arcs between the points.

Title | extremal |
---|---|

Canonical name | Extremal |

Date of creation | 2013-03-22 19:10:29 |

Last modified on | 2013-03-22 19:10:29 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 4 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 47A60 |

Synonym | extremal curve |

Related topic | CalculusOfVariations |

Defines | extremal function |