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We obtain an upper bound on the lowest magnetic Neumann eigenvalue of abounded, convex, smooth, planar domain with moderate intensity of thehomogeneous magnetic field. This bound is given as a product of a purelygeometric factor expressed in terms of the torsion function and of the lowestmagnetic Neumann eigenvalue of the disk having the same maximal value of thetorsion function as the domain. The bound is sharp in the sense that equalityis attained for disks. Furthermore, we derive from our upper bound that thelowest magnetic Neumann eigenvalue with the homogeneous magnetic field ismaximized by the disk among all ellipses of fixed area provided that theintensity of the magnetic field does not exceed an explicit constant dependentonly on the fixed area.

A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function