Are the Kantorovitch polynomials area diminishing? (Q930121)

The Bernstein-Bézier polynomials are known to possess total variation and length diminishing properties in one variable. The two-dimensional generalizations to the square and the triangle are investigated. Simple counterexamples show that they do not diminish surface area. The Kantorovitch polynomials are considered which seem to be a better choice to be area diminishing. A counterexample is given for the square. Then the Kantorovitch polynomials on the triangle are defined and an area estimate for them is given.