An Improved Energy-Area Inequality for Harmonic Maps Using Image Curvature
arXiv:math/0407499
Abstract
An ODE variational calculation shows that an image principle curvature ratio factor can raise the lower bound, 2(Image Area), on energy of a harmonic map of a surface into Rn. In certain situations, including all radially symmetry harmonic maps, equality is achieved.
v1: 8 pages, 1 figure. (Thm 2 proof wrong & counter example found to Cor 3) v2=v3: 6 pages 1 figure