Integral geometry for the 1-norm


Venue   Convex and Integral Geometry, Goethe-Universität, Frankfurt, 26 September 2011.

Abstract   Classical integral geometry takes place in Euclidean space, but one can attempt to imitate it in any other metric space. In particular, one can attempt this in Rn equipped with the metric derived from the p-norm. This has been thoroughly investigated for 1 < p < ∞, but not for p = 1 .

Integral geometry for the 1-norm (in the metric sense above) bears a striking resemblance to integral geometry for the 2-norm, but is radically different from that for all other values of p. I will give a Hadwiger-type theorem for Rn with the 1-norm, and analogues of the classical formulas of Steiner, Crofton and Kubota. I will also give principal and higher kinematic formulas. Each of these results is closely analogous to its Euclidean counterpart, yet the proofs are quite different.

Slides   In this pdf file

Paper   Integral geometry for the 1-norm, arXiv:1012.5881

Post   Hadwiger's theorem, part 2

This page was last changed on 5 October 2011. You can read an extremely short introduction to Beamer, or go home.