Rotational Elliptic Weingarten surfaces in S2xR and the Hopf problem

TL;DR

This paper proves that all uniformly elliptic Weingarten spheres in S2xR are congruent to a canonical example, using bounded second fundamental form and a Hopf-type result.

Contribution

It establishes a classification of elliptic Weingarten spheres in S2xR, extending the understanding of their geometric properties and uniqueness.

Findings

Uniformly elliptic Weingarten spheres are congruent to canonical examples.

Rotational elliptic Weingarten surfaces in S2xR have bounded second fundamental form.

A Hopf-type result is proved for these surfaces.

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. G\'alvez and P. Mira.