In this paper, we investigate the relationships between linear measure and harmonic mappings. Firstly, we obtain the sharp linear measure distortion theorem of the image of any measurable subset of the unit circle under sense-preserving and univalent harmonic mappings. Secondly, we establish a Schwarz type lemma of K-quasiconformal harmonic mappings, and give a characterization of M-Lavrentiev domains by using K-quasiconformal harmonic mappings. Finally, we discuss coefficient estimates on a class of K-qua...
