In the plane, (d^{(l_p)}(A))^p is subadditive under Minkowski sums up to the sharp factor max{1, 2^{p-2}}.
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A sharp $p$-subadditive bound for the $l_p$ Hausdorff distance from convex hull
In the plane, (d^{(l_p)}(A))^p is subadditive under Minkowski sums up to the sharp factor max{1, 2^{p-2}}.