Recently, Eisenbrand, Pach, Rothvoß, and Sopher studied the function M(m, n), which is the largest cardinality of a convexly independent subset of the Minkowski sum of some planar point sets P and Q with |P | = m and |Q| = n. They proved that M(m, n) = O(m2/3n2/3+m+n), and asked whether a superlinear lower bound exists for M(n, n). In this note, we show that their upper bound is the best possib...

Article history: Available online 17 July 2008

3 Proof of Theorem 1 9 3.1 Estimation of the g1 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Estimation of the g3 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Estimation of the g2 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Putting everything together. . . . . . . . . . . . . . . . . . . . . ....

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