Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Mean curvature flow with triple junctions in higher space dimensions

We consider mean curvature flow of n-dimensional surface clusters. At (n-1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120 degree angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hoelder spaces.Comment: 31 pages, 2 figure

Determination of fungal activity in modified wood by means of micro-calorimetry and determination of total esterase activity

Beech and pine wood blocks were treated with 1,3-dimethylol-4,5-dihydroxyethylen urea (DMDHEU) to increasing weight percent gains (WPG). The resistance of the treated specimens against Trametes versicolor and Coniophora puteana, determined as mass loss, increased with increasing WPG of DMDHEU. Metabolic activity of the fungi in the wood blocks was assessed as total esterase activity (TEA) based on the hydrolysis of fluorescein diacetate and as heat or energy production determined by isothermal micro-calorimetry. Both methods revealed that the fungal activity was related with the WPG and the mass loss caused by the fungi. Still, fungal activity was detected even in wood blocks of the highest WPG and showed that the treatment was not toxic to the fungi. Energy production showed a higher consistency with the mass loss after decay than TEA; higher mass loss was more stringently reflected by higher heat production rate. Heat production did not proceed linearly, possibly due to the inhibition of fungal activity by an excess of carbon dioxide

Bumble bee parasite strains vary in resistance to phytochemicals

Nectar and pollen contain diverse phytochemicals that can reduce disease in pollinators. However, prior studies showed variable effects of nectar chemicals on infection, which could reflect variable phytochemical resistance among parasite strains. Inter-strain variation in resistance could influence evolutionary interactions between plants, pollinators, and pollinator disease, but testing direct effects of phytochemicals on parasites requires elimination of variation between bees. Using cell cultures of the bumble bee parasite Crithidia bombi, we determined (1) growth-inhibiting effects of nine floral phytochemicals and (2) variation in phytochemical resistance among four parasite strains. C. bombi growth was unaffected by naturally occurring concentrations of the known antitrypanosomal phenolics gallic acid, caffeic acid, and chlorogenic acid. However, C. bombi growth was inhibited by anabasine, eugenol, and thymol. Strains varied >3-fold in phytochemical resistance, suggesting that selection for phytochemical resistance could drive parasite evolution. Inhibitory concentrations of thymol (4.53-22.2 ppm) were similar to concentrations in Thymus vulgaris nectar (mean 5.2 ppm). Exposure of C. bombi to naturally occurring levels of phytochemicals—either within bees or during parasite transmission via flowers—could influence infection in nature. Flowers that produce antiparasitic phytochemical, including thymol, could potentially reduce infection in Bombus populations, thereby counteracting a possible contributor to pollinator decline