A note on Willmore minimizing Klein bottles in Euclidean space

We show that φ∘τ˜3,1:K→R4×{0}n−4 is the unique minimizer among immersed Klein bottles in its conformal class, where φ:S4→R4 is a stereographic projection and τ˜3,1 is the bipolar surface of Lawson's τ3,1-surface [11]. We conjecture that φ∘τ˜3,1 is the unique minimizer among immersed Klein bottles into Rn, n≥4, whose existence the authors and P. Breuning proved in [2].