Quasiconformal Maps and Substantial Boundary Points
نویسنده
چکیده
Let D be a bounded domain in C with ζ0 ∈ ∂D. We say that ζ0 is a substantial boundary point of D for the affine stretch x+ iy 7→ Kx+ iy, where K > 1, if for every neighbourhood U of ζ0 and for every component V of U ∩ D with ζ0 ∈ ∂V , the maximal dilatation of f is at least K for every quasiconformal map f of V such that f(x+ iy) = Kx+ iy for all x+ iy ∈ ∂V ∩ ∂D. We give here a criterion for a point ζ0 to be a substantial boundary point for the affine stretch in D — Theorem 1.1 below. This will depend on the “narrowness” ofD near ζ0 though the particular way that D is narrow may vary, as we shall show.
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