A note on the compression theorem for convex surfaces. (English) Zbl 0986.90047

Weng, J. F.; Rubinstein, J. H.

Discrete Math. 212, No. 3, 257-260 (2000).

Summary: Suppose \(a_ib_ic_i\) \((i= 1,2)\) are two triangles of equal side lengths and lying on sphere \(\Phi_i\) with radii \(r_1\), \(r_2\) \((r_1< r_2)\), respectively. We have proved that there is a continuous map \(h\) of \(a_1b_1c_1\) onto \(a_2b_2c_2\) so that for any two points \(p\), \(q\) in \(a_1b_1c_1\), \(|pq|\geq|h(p)h(q)|\) [J. H. Rubinstein and J. F. Weng, J. Comb. Optimization 1, 67-78 (1997; Zbl 0895.90173)]. In this note we generalize this compression theorem to convex surfaces.

MSC:

90C27	Combinatorial optimization
90C35	Programming involving graphs or networks

Keywords:

compression theorem; convex surface; continuous map; comparison theorem

Citations:

Zbl 0895.90173