Curved, extended classical solutions I. The undulating kink
  The energy of extended classical objects, such as vortices, depends on their shape. In particular, we show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. We obtain a closed form for the curvature energy, assuming small deviations from the straight line. 
A. Herat, R. Rademacher, and P. Suranyi