Constrained Willmore Surfaces

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of immersions under the constraint that the admissible variations infinitesimally preserve the conformal structure. Besides constrained Willmore surfaces we discuss in some detail examples of constrained minimal and volume critical surfaces, the critical points of the area and enclosed volume functional under the conformal constraint.Comment: 17 pages, 8 figures; v2: Hopf tori added as an example, minor changes in presentation, numbering changed; v3: new abstract and appendix, several changes in presentatio

Dental caries in rats associated with Candida albicans

In addition to occasional opportunistic colonization of the oral mucosa, Candida albicans is frequently found in carious dentin. The yeast's potential to induce dental caries as a consequence of its pronounced ability to produce and tolerate acids was investigated. Eighty caries-active Osborne-Mendel rats were raised on an ampicillin-supplemented diet and exposed to C. albicans and/or Streptococcus mutans, except for controls. Throughout the 28-day test period, the animals were offered the modified cariogenic diet 2000a, containing 40% various sugars. Subsequently, maxillary molars were scored for plaque extent. After dissection, the mandibular molars were evaluated for smooth surface and fissure caries. Test animals exposed to C. albicans displayed considerably more advanced fissure lesions (p < 0.001) than non-exposed controls. While S. mutans yielded similar results, a combined association of C. albicans and S. mutans had no effect on occlusal caries incidence. Substituting dietary sucrose by glucose did not modify caries induction by C. albicans. However, animals fed a diet containing 20% of both sugars showed no differences to non-infected controls. Smooth surface caries was not generated by the yeast. This study provides experimental evidence that C. albicans is capable of causing occlusal caries in rats at a high rate