Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
On the energy of quasiconformal mappings and pseudoholomorphic curves in complex projective spaces
Hervé GaussierMasaki Tsukamoto
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2022 Volume 74 Issue 2 Pages 427-446

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Abstract

We prove that the energy density of uniformly continuous, quasiconformal mappings, omitting two points in ℂℙ1, is equal to zero. We also prove the sharpness of this result, constructing a family of uniformly continuous, quasiconformal mappings, whose areas grow asymptotically quadratically. Finally, we prove that the energy density of pseudoholomorphic Brody curves, omitting three “complex lines” in general position in ℂℙ2, is equal to zero.

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