Let $D$ be a bounded open subset of $\erre^N$ and let $z_0$ be a point of $D$. Assume that the Newtonian potential of $D$ is proportional outside $D$ to the potential of a mass concentrated at $z_0$. Then $D$ is a Euclidean ball centred at $z_0$. This theorem, proved by Aharonov, Schiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we extend the Suzuki–Watson Theorem to a class of hypoellliptic operators of Kolmogorov-type.
ON A RIGIDITY RESULT FOR KOLMOGOROV-TYPE OPERATORS
Kogoj
2024
Abstract
Let $D$ be a bounded open subset of $\erre^N$ and let $z_0$ be a point of $D$. Assume that the Newtonian potential of $D$ is proportional outside $D$ to the potential of a mass concentrated at $z_0$. Then $D$ is a Euclidean ball centred at $z_0$. This theorem, proved by Aharonov, Schiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we extend the Suzuki–Watson Theorem to a class of hypoellliptic operators of Kolmogorov-type.File in questo prodotto:
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