Removability theorems for Sobolev functions and quasiconformal maps (Q1426911)

Several sufficient conditions for a set to be (quasi)conformally removable and Sobolev removable are established. The (quasi)conformally removable and the Sobolev removable play very important roles in the holomorphic dynamics. Therefore the authors have given the applications of these two ideas in the holomorphic dynamics. We notice that the authors are mostly interested in the planar case, where all their theorems are considered.