Estimate for Heinz Inequality in the Small Dilatation of Harmonic Quasiconformal Mappings
Let w(z) be a harmonic K-quasiconformal self-mapping of the unit disk satisfying w(0) = 0, then Heinz inequality can be improved as vertical bar w(z)(0)vertical bar(2) + vertical bar w((z) over bar)(0)vertical bar(2) >= max {M(K), 27/4 pi(2)}, where M(K) is a strictly decreasing function of K. Moreover, if K is an element of [1, 1.03], the previous corresponding results in [3] are improved.
heinz inequality quasiconformal mapping harmonic mapping harmonic quasi-invariant measure schwarz lemma