Annales Academię Scientiarum Fennicę
Volumen 35, 2010, 3-21


Neil N. Katz

New York City College of Technology, Mathematics Department
300 Jay Street, Brooklyn, NY 11201, U.S.A.; nkatz 'at'

Abstract. In this paper a modulus of curves is defined using pseudo-distance functions. This leads to a notion of quasiconformal maps that is equivalent to the standard definition when the distance function is Riemannian. The moduli of families of curves whose endpoints lie in the boundary of open subsets of a compact, convex set are determined. This allows bounds on volumes of images of Euclidean balls under quasiconformal maps to be made. Also, certain generalized, conformal, isosystolic constants are found. Estimates are given of how these constants, and of how norms of weak upper gradients, vary under quasiconformal maps.

2000 Mathematics Subject Classification: Primary 30C65, 53C23, 53C65.

Key words: Quasiconformal maps, volume distortion, conformal isosystolic inequalities, conformal filling volume.

Reference to this article: N.N. Katz: A modulus for curves from distance. Ann. Acad. Sci. Fenn. Math. 35 (2010), 3-21.

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