Al Baernstein and Stephen Montgomery-Smith, Some conjectures about integral means of \(\partial f\) and \(\bar\partial f\).
Complex Analysis and Differential Equations, edited by C.Kiselman, Acta Universitatis Upsaliensis C., Volume 64 (1999), 92-109.
We discuss some conjectural inequalities concerning a problem from the calculus of variations, namely that rank 1 convex functions are quasi-convex. An affirmative answer would also give the best constants for the Beurling-Ahlfors operator that appears in the theory of quasi-conformal mappings on the plane.
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