Blackfolds, plane waves and minimal surfaces

Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.

Mandibula wing osteotomy for correction of the mandibular plane: A case report

We report a new technique for vertical enlargement of the inferior border of the mandible.

Chondrocyte function after osteochondral transfer: comparison of concave and plane punches

An incongruity between instrument and articular surfaces in osteochondral transfer (OCT) results in unevenly distributed impact forces exerted on the cartilage which may cause a loss of functional chondrocytes. We tested whether a plane instead of a concave design of the punch of an osteotome can reduce these cartilage damages.

Coronal plane segmental flexibility in thoracic adolescent idiopathic scoliosis assessed by fulcrum-bending radiographs

Knowledge about segmental flexibility in adolescent idiopathic scoliosis is crucial for a better biomechanical understanding, particularly for the development of fusionless, growth-guiding techniques. Currently, there is lack of data in this field. The objective of this study was, therefore, to compute segmental flexibility indices (standing angle minus corrected angle/standing angle). We compared segmental disc angles in 76 preoperative sets of standing and fulcrum-bending radiographs of thoracic curves (paired, two-tailed t tests, p < 0.05). The mean standing Cobb angle was 59.7 degrees (range 41.3 degrees -95 degrees ) and the flexibility index of the curve was 48.6\% (range 16.6-78.8\%). The disc angles showed symmetric periapical distribution with significant decrease (all p values <0.0001) for every cephalad (+) and caudad (-) level change. The periapical levels +1 and -1 wedged at 8.3 degrees and 8.7 degrees (range 3.5 degrees -14.8 degrees ), respectively. All angles were significantly smaller on the-bending views (p values <0.0001). We noted mean periapical flexibility indices of 46\% (+1), 49\% (-1), 57\% (+2) and 81\% (-2), which were significantly less (p < 0.001) than for the group of remote levels 105\% (+3), 149\% (-3), 231\% (+4) and 300\% (-4). The discal and bony wedging was 60 and 40\%, respectively, and mean values 35 degrees and 24 degrees (p < 0.0001). Their relationship with the Cobb angle showed a moderate correlation (r = 0.56 and 0.45). Functional, radiographic analysis of idiopathic thoracic scoliosis revealed significant, homogenous segmental tethering confined to four periapical levels. Future research will aim at in vivo segmental measurements in three planes under defined load to provide in-depth data for novel therapeutic strategies.