Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry

This paper is devoted to the study of a fundamental problem in the theory of quasiconformal analysis: under what conditions local quasiconformality of a homeomorphismimplies its global quasisymmetry. In particular, we introduce the concept of weak (L,M)-quasisymmetry, serving as a bridge between local quasiconformality and global quasisymmetry.