منابع مشابه
On Quasiconformal Harmonic Maps between Surfaces
It is proved the following theorem, if w is a quasiconformal harmonic mappings between two Riemann surfaces with smooth boundary and aproximate analytic metric, then w is a quasi-isometry with respect to Euclidean metric.
متن کاملQuasiconformal Harmonic Maps into Negatively Curved Manifolds
Let F : M → N be a harmonic map between complete Riemannian manifolds. Assume that N is simply connected with sectional curvature bounded between two negative constants. If F is a quasiconformal harmonic diffeomorphism, then M supports an infinite dimensional space of bounded harmonic functions. On the other hand, if M supports no non-constant bounded harmonic functions, then any harmonic map o...
متن کاملComputing Extremal Quasiconformal Maps
Conformal maps are widely used in geometry processing applications. They are smooth, preserve angles, and are locally injective by construction. However, conformal maps do not allow for boundary positions to be prescribed. A natural extension to the space of conformal maps is the richer space of quasiconformal maps of bounded conformal distortion. Extremal quasiconformal maps, that is, maps min...
متن کاملBilipschitz Approximations of Quasiconformal Maps
We show that for any K -quasiconformal map of the upper half plane to itself and any ε > 0 , there is a (K + ε) -quasiconformal map of the half plane with the same boundary values which is also biLipschitz with respect to the hyperbolic metric.
متن کاملOn Harmonic Quasiconformal Self-mappings of the Unit Ball
It is proved that any family of harmonic K-quasiconformal mappings {u = P [f ], u(0) = 0} of the unit ball onto itself is a uniformly Lipschitz family providing that f ∈ C. Moreover, the Lipschitz constant tends to 1 as K → 1.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1998
ISSN: 0030-8730
DOI: 10.2140/pjm.1998.182.359