A Jordan curve in \(\mathbb C\) is called a quasicircle if it is the image of the unit circle by a quasiconformal self-mapping of \(\mathbb C\) . While a lot of characterizations of quasicircles are known, we are interested in the characterization by an extendability condition on Dirichlet finite harmonic functions. Recently, Schippers and Staubach consider quasicircles on compact Riemann surfaces and characterize the circles by the extendability condition. In this paper, we present a generalization of their result which will be given in our forthcoming paper. We also discuss some further problems.