Rotational Elliptic Weingarten surfaces in S2xR and the Hopf problem

Abstract

We prove that any uniformly elliptic Weingarten (topological) sphere in S2xR must be congruent to the canonical example associated to the Weingarten equation. The result is obtained by proving that rotational uniformly elliptic Weingarten surfaces in S2xR have bounded second fundamental form together with a Hopf type result by J. A. Gálvez and P. Mira.