An Improved Energy-Area Inequality for Harmonic Maps Using Image Curvature

Details An Improved Energy-Area Inequality for Harmonic Maps Using Image Curvature An Improved Energy-Area Inequality for Harmonic Maps Using Image Curvature

2004-07-28

arxiv.org/abs/math/0407499v3

Mathematics

Differential Geometry

v1: 8 pages, 1 figure. (Thm 2 proof wrong & counter example found to Cor 3) v2=v3: 6 pages 1 figure

Scientific paper

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.

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