For more information about this meeting, contact Stephanie Zerby.

Title: | Minimality of planes and a new formula for the area of a polygon |

Seminar: | Geometry Luncheon Seminar |

Speaker: | Sergey Ivanov |

Abstract: |

I will talk about the following result (joint with Dima Burago).
Let X be a finite-dimensional normed space and D a two-dimensional disc
lying in an affine plane in X. Then D has the least area among all compact
surfaces in X having the same boundary. (The area of a surface in X is
defined as the two-dimensional Hausdorff measure.) Although this fact
looks obvious, it was an open problem since 1960s and remains open for
surfaces of dimension greater than 2. The key ingredient of the proof is
an elementary formula for the
(Euclidean) area of a central symmetric polygon in the plane in terms of
areas of parallelograms circumscribed about it. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 04 / 11 / 2012 |

Time: | 12:15pm - 01:30pm |