Collars and partitions of hyperbolic cone-surfaces

For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than $\pi$ to be able to consider partitions.Comment: 11 pages, 9 figures; v2: minor changes, to appear in Geometriae Dedicat

Relation of Structure to the Microhardness of Human Dentin

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66589/2/10.1177_00220345590380032701.pd

Analytic functions satisfying Holder conditions on the boundary

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23936/1/0000183.pd

Definitions of quasiconformality

We establish that the infinitesimal “ H -definition” for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even in R n where we obtain that the “limsup” condition in the H -definition can be replaced by a “liminf” condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-arc surfaces is also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46582/1/222_2005_Article_BF01241122.pd