A Remark on Harmonic Quasiconformal Mappings

概要

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K-quasiconformal mappings of Riemann surfaces was investigated by P.J. Kiernan in [2]. One of his interesting results is that harmonic K-quasiconformal mappings of certain Riemann surfaces are distance-decreasing. We shall discuss here harmonic K-quasiconformal mappings of n-dimensional Riemannian manifolds and generalize the above Kiernan's theorem to this case. In section 1 we review the theory of harmonic forms as found in [4]. Section 2 is devoted to get some lemmas which are used to prove our theorem in the last section. Concerning quasiconformal mappings, we use the fact given by H. Wu in [5].
徳島大学の論文