Mappings of finite distortion: Formation of exponential cusp

Details Mappings of finite distortion: Formation of exponential cusp Mappings of finite distortion: Formation of exponential cusp

2010-05-17

arxiv.org/abs/1005.2842v1

Mathematics

Complex Variables

8 pages

Scientific paper

We consider a quasi-convex planar domain \Omega with a rectifiable boundary
containing an exponential cusp and show that there is no homeomorphism f:
\bR^2\to\bR^2 of finite distortion with \exp(\lambda K)\in L_{loc}^{1}(\bR^2)
for some \lambda>0 such that f(B)=\Omega. On the other hand, if we only require
that K_f(x)\in L_{loc}^{p}(\bR^2), then such an f exists.

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