论文信息 - A Set Containing Recfiable Arcs QC-locally But Not QC-globally - 字舞流文

A Set Containing Recfiable Arcs QC-locally But Not QC-globally

We construct a Sierpinski carpet E ⊂ R2 of area zero and a K0 > 1 with the property that every K0-quasiconformal image of E contains rectifiable curves, but such that E has some quasiconformal image containing no non-constant rectifiable curves.

Christopher J. Bishop

[1] Charles M. Bishop,et al. Harmonic measure,L2-estimates and the Schwarzian derivative , 1994 .

[2] S. Semmes. Bilipschitz mappings and strong weights. , 1992 .

[3] J. Heinonen,et al. Thirty-three yes or no questions about mappings, measures, and metrics , 1997 .

[4] Peter W. Jones. Rectifiable sets and the Traveling Salesman Problem , 1990 .

[5] The quasiconformal Jacobian problem , 2006 .

[6] Juha Heinonen,et al. Geometric embeddings of metric spaces , 2003 .

[7] J. Cassels,et al. An Introduction to Diophantine Approximation , 1957 .

[8] Donald E. Marshall,et al. Harmonic Measure: Jordan Domains , 2005 .

[9] Christopher J. Bishop,et al. Harmonic measure and arclength , 1990 .

[10] Julia Heinonent. The Branch Set of a Quasiregular Mapping , 2002 .

[11] K. Okikiolu. Characterization of Subsets of Rectifiable Curves in Rn , 1992 .

[12] The Traveling Salesman problem and Harmonic analysis , 1991 .