Integral-Geometric Formulas for Perimeter in $\S^2$, $\H^2$ and Hilbert Planes
Integral-Geometric Formulas for Perimeter in $\S^2$, $\H^2$ and Hilbert Planes
We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Specializing to H 2 we get a formula that appears to be new. In the projective model of H 2 we have …