A note on the compression theorem for convex surfaces

Abstract

Suppose aibici (i = 1,2) are two triangles of equal side lengths and lying on spheres Φi with radii r1, r2 (r1 < r2), respectively. We have proved that there is a continuous map h of a1b1c1 onto a2b2c2 so that for any two points p, q in a1b1c1, |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. © 2000 Elsevier Science B.V. All rights reserved.