A note on the compression theorem for convex surfaces

Abstract

Suppose a ib ic i (i=1,2) are two triangles of equal side lengths and lying on spheres Φ i with radii r 1,r 2 (r 1<r 2) , respectively. We have proved that there is a continuous map h of a 1 b 1 c 1 onto a 2 b 2 c 2 so that for any two points p, q in a 1b 1c 1, |pq|⩾|h(p)h(q)| (Rubinstein and Weng, J. Combin. Optim. 1 (1997) 67–78). In this note we generalize this compression theorem to convex surfaces.