Quasiconvexity in the Heisenberg group |
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| Authors: | David A. Herron Anton Lukyanenko Jeremy T. Tyson |
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| Affiliation: | 1.Department of Mathematical Sciences,University of Cincinnati,Cincinnati,USA;2.Department of Mathematics,University of Michigan,Ann Arbor,USA;3.Department of Mathematics,University of Illinois,Urbana,USA |
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| Abstract: | We show that if A is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of A is quasiconvex. In particular, closed sets which are null sets for the cc-Hausdorff 3-measure have quasiconvex complements. Conversely, we exhibit a compact totally disconnected set of Hausdorff dimension three whose complement is not quasiconvex. |
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