
Venue
Convex and
Integral Geometry,
GoetheUniversität,
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 R^{n} equipped with the metric derived from the pnorm. This has been thoroughly investigated for 1 < p < ∞, but not for p = 1 . Integral geometry for the 1norm (in the metric sense above) bears a striking resemblance to integral geometry for the 2norm, but is radically different from that for all other values of p. I will give a Hadwigertype theorem for R^{n} with the 1norm, 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 1norm, arXiv:1012.5881 Post Hadwiger's theorem, part 2
