This talk is devoted to some fundamental problems on quasi-extremal distance constant, modulus of curve families, n-harmonic function and their relations to nonlinear degenerate elliptic equation. We obtain the existence, uniqueness and boundary behavior of the extremal function for the capacity of a capacitor in R^n. Furthermore, we get a decomposition for the extremal length of curve family joining two disjoint continua in R^n. With the help of results mentioned above, we finally establish a sharp upper bound for the quasi-extremal distance constant of a domain in terms of its local boundary quasiconformal reflection constant.

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