Let M be a compact, connected, orientable, hyperbolic 3-manifold whose boundary is a torus. We show that there are at most five slopes on ∂M whose associated Dehn fillings have either a finite or an infinite cyclic fundamental group. Furthermore, the distance between two slopes yielding such manifolds is no more than three, and there is at most one pair of slopes which realize the distance three. Each of these bounds is realized when M is taken to be the exterior of the figure-8 sister knot.
PURPOSE. To conduct in vivo measurements of the bulbar conjunctiva epithelial, stromal, and total thicknesses in healthy Chinese subjects using optical coherence tomography (OCT) and to compare the conjunctival thickness differences between sex and age.METHODS. From January to July 2012, healthy Chinese subjects were recruited to undergo a Cirrus HD-OCT examination using the Anterior Segment 5 Line Raster scanning protocol. Ophthalmoscopy and slit-lamp examinations were performed on all eyes, along with the determination of visual acuity. The bulbar conjunctiva epithelial thickness, stromal thickness, and full thickness were measured on cross-sectional conjunctiva images. The average values of each parameter were compared between males and females and among eight age groups (<20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, and >80 years).
RESULTS.A total of 711 eyes in 711 subjects (average age 46.5 years) were included. The average conjunctiva epithelial, stromal, and full thickness measurements were 42.4 6 7.4 lm, 197.7 6 32.5 lm, and 240.1 6 29.8 lm, respectively. No significant difference was found for any of the three parameters between sexes. The conjunctiva epithelial thickness values decreased significantly after age 20 and were then maintained at relatively low levels, followed by a sharp increase at 60 years of age. The conjunctiva stromal thickness decreased throughout the entire lifetime, and the full thickness decreased from the teenage to the elderly periods.CONCLUSIONS. None of the Chinese conjunctiva epithelial, stromal, and full thickness was sexrelated, but all of them were age-related.
Let M be a one-cusped hyperbolic 3-manifold. A slope on the boundary of the compact core of M is called exceptional if the corresponding Dehn filling produces a non-hyperbolic manifold. We give new upper bounds for the distance between two exceptional slopes˛andˇin several situations. These include cases where M.ˇ/ is reducible and where M.˛/ has finite 1 , or M.˛/ is very small, or M.˛/ admits a 1 -injective immersed torus. 57M25, 57M50, 57M99
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