Any isometry between the spheres of absolutely smooth 2-dimensional Banach spaces is linear (Q2661267)

The author provides a partial solution to the famous problem of Tingley by proving the following result: if \(X\) and \(Y\) are two-dimensional, absolutely smooth Banach spaces, then every isometry between their unit spheres \(S_X\) and \(S_Y\) can be extended to a linear isometry between \(X\) and \(Y\).