6,453 research outputs found
A note on quasiconformal maps with Holder-continuous dilatation
Here we give an alternate proof of a sufficient condition due to J. Mateu, J.
Orobitg, and J. Verdera for a quasiconformal map of the plane with dilatation
supported in a smooth domain to be bi-Lipschitz. We also extend this theorem to
cover boundaries with certain types of corners.Comment: 13 pages, 2 figure
Discrete Approximations of Metric Measure Spaces of Controlled Geometry
We find a necessary and sufficient condition for a doubling metric space to
carry a (1,p)-Poincare inequality. The condition involves discretizations of
the metric space and Poincare inequalities on graphs.Comment: 23 Page
Delaware Physicians\u27 Behavior Regarding Patient Advice on Tobacco Use
No abstract available
Quasisymmetry and rectifiability of quasispheres
We obtain Dini conditions with "exponent 2" that guarantee that an
asymptotically conformal quasisphere is rectifiable. In particular, we show
that for any e>0 integrability of
(esssup_{1-t < |x| < 1+t} K_f(x)-1)^{2-e} dt/t implies that the image of the
unit sphere under a global quasiconformal homeomorphism f is rectifiable. We
also establish estimates for the weak quasisymmetry constant of a global
K-quasiconformal map in neighborhoods with maximal dilatation close to 1.Comment: 19 pages, 3 figures (version 3: minor changes and typos fixed
Self-consistent solutions of canonical proper self-gravitating quantum systems
Generic self-gravitating quantum solutions that are not critically dependent
on the specifics of microscopic interactions are presented. The solutions
incorporate curvature effects, are consistent with the universality of gravity,
and have appropriate correspondence with Newtonian gravitation. The results are
consistent with known experimental results that indicate the maintenance of the
quantum coherence of gravitating systems, as expected through the equivalence
principle.Comment: 13 pages, 7 figure
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