On a rigidity result for Kolmogorov-type operators

Let D be a bounded open subset of R^n and let z be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z. Then D is a Euclidean ball centred at z. This theorem, proved by Aharonov, Shiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this seminar, we show that the Suzuki–Watson Theorem is a particular case of a more general rigidity result related to a class of hypoellliptic operators of Kolmogorov-type. Talk based on joint work with E.Lanconelli.