PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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