Conformal Willmore tori in ?4

摘要

For every two-dimensional torus T 2 {T^{2}} and every k ∈ in ? mathbb{N} , k ≥ 3 {kgeq 3} , we construct a conformal Willmore immersion f : T 2 T^{2} → o ? 4 mathbb{R}^{4} with exactly one point of density k and Willmore energy 4πk. Moreover, we show that the energy value 8 ? π {8pi} cann