The natural distribution of Cycas micronesica includes three island groups. Damage to the widespread tree from the armored scale Aulacaspis yasumatsui was initiated with the 2003 invasion of Guam and the 2007 invasion of Rota. This herbivore has threatened the unique gymnosperm species with extinction. The number and identity of co-occurring consumers are dissimilar among disjunct insular subpopulations, and six of these habitats were used to assess tree mortality trends to confirm that A. yasumatsui stands alone as the greatest threat to species persistence. Following the initial infestation outbreak of this pest into each new subpopulation, the standing seedlings and saplings were the first to be culled, the juvenile plants were the next to be culled, and then the adult trees were killed more slowly thereafter. The timing of this plant population behavior did not differ among habitats with five other consumers, three other consumers, one other consumer, or no other consumers. We have shown that A. yasumatsui acting as the sole biotic threat in an isolated subpopulation can generate a decline in survival that is as rapid as when it is acting in conjunction with up to five other consequential consumers. This armored scale is the most acute threat to C. micronesica, and adding other specialist herbivores to the scale herbivory does not alter the speed and extent of initial plant mortality.
Christoph Lehrenfeld, Gert Lube, Philipp W. Schroeder
AbstractNowadays, (high‐order) DG methods, or hybridised variants thereof, are widely used in the simulation of turbulent incompressible flow problems. For turbulence simulations, and especially in the practically relevant situation of strong under‐resolution, it is important to distinguish between the resolved physical dissipation rate and the contribution of numerical dissipation originating from the underlying method. In this note, a certain ambiguity related to such a decomposition for the viscous effects in a DG‐discretised fluid flow problem, which is due to the discontinuity of the approximate solution, is addressed. A novel but rather natural decomposition into ‘physical’ and ‘numerical’ viscous dissipation is proposed for a class of DG methods. Based on a typical 3D benchmark problem for decaying turbulence, its meaningfulness is confirmed numerically. In order to justify the term ‘dissipation’, both the physical and the numerical contributions for the proposed additive decomposition are provably non‐negative (possibly zero).
We lay down an elementary yet fundamental lemma concerning a finite algebraicness property of a smooth map from an Azumaya/matrix manifold with a fundamental module to a smooth manifold. This gives us a starting point to build a synthetic (synonymously, $C^{\infty}$-algebraic) symplectic geometry and calibrated geometry that are both tailored to and guided by D-brane phenomena in string theory and along the line of our previous works D(11.1) (arXiv:1406.0929 [math.DG]) and D(11.2) (arXiv:1412.0771 [hep-th]).
We apply the general theory of codimension one integrability conditions for $G$-structures developed in arXiv:1306.6817v3 [math.DG] to the case of quaternionic CR geometry. We obtain necessary and sufficient conditions for an almost CR quaternionic manifold to admit local immersions as an hypersurface of the quaternionic projective space. We construct a deformation of the standard quaternionic contact structure on the quaternionic Heisenberg group which does not admit local immersions in any quaternionic manifold.
In view of Andreotti and Grauert (Bull Soc Math France 90:193–259, 1962) vanishing theorem for $$q$$-complete domains in $$\mathbb C ^{n}$$, we reprove a vanishing result by Sha (Invent Math 83(3):437–447, 1986), and Wu (Indiana Univ Math J 36(3):525–548, 1987), for the de Rham cohomology of strictly $$p$$-convex domains in $$\mathbb R ^n$$ in the sense of Harvey and Lawson (The foundations of $$p$$-convexity and $$p$$-plurisubharmonicity in riemannian geometry. arXiv:1111.3895v1 [math.DG]). Our proof uses the $${L}^2$$-techniques developed by Hörmander (An introduction to complex analysis in several variables, 3rd edn. North-Holland Publishing Co, Amsterdam 1990), and Andreotti and Vesentini (Inst Hautes Études Sci Publ Math 25:81–130, 1965).
In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and Kreussler-Kurke to the case of arbitrary signature. In particular, the branch divisor of the double covering is a cut of the rational threefold by a single quartic hypersurface. A defining equation of the hypersurface is determined in an explicit form. We also show that these twistor spaces interpolate LeBrun twistor spaces and the twistor spaces constructed in math.DG/0701278.
In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and Kreussler-Kurke to the case of arbitrary signature. In particular, the branch divisor of the double covering is a cut of the rational threefold by a single quartic hypersurface. A defining equation of the hypersurface is determined in an explicit form. We also show that these twistor spaces interpolate LeBrun twistor spaces and the twistor spaces constructed in math.DG/0701278.
In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications is an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years. This paper summarizes the work in the papers arXiv:1005.3845 [math.DG] and arXiv:1008.1757 [math.DG].
The existence of a natural and projectively invariant quantization in the sense of P. Lecomte (Progr. Theoret. Phys. Suppl. (2001), no. 144, 125{132) was proved by M. Bor- demann (math.DG/0208171), using the framework of Thomas{Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n + 1jm)-equivariant quantization on R njm constructed by P. Mathonet and F. Radoux in (arXiv:1003.3320). Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in (arXiv:0909.5419) for symbols of degree two.
Abstract Nurowski [P. Nurowski, Is dark energy meaningless?, arXiv:1003.1503 [math.DG]] has recently suggested a link between the observation of dark energy in cosmology and the projective equivalence of certain Friedman–Lemaitre–Robertson–Walker (FLRW) metrics. Specifically, he points out that two FLRW metrics with the same unparameterized geodesics have their energy densities differing by a constant. From this he queries whether the existence of dark energy is meaningful. We point out that physical observables in cosmology are not projectively invariant and we relate the projective symmetry uncovered by Nurowski to some previous work on projective equivalence in cosmology.
Given a family of smooth immersions $F_t: M^n\to N^{n+1}$ of closed hypersurfaces in a locally symmetric Riemannian manifold $N^{n+1}$ with bounded geometry, moving by the mean curvature flow, we show that at the first finite singular time of the mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a recent result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of N. Le in the Euclidean case (arXiv: math.DG/1002.4669v2).
In this paper, we will study the existence problem of min-max minimal torus. We use classical conformal invariant geometric variational methods. We prove a theorem about the existence of min-max minimal torus in Theorem 5.1. First we prove a strong uniformization result (Proposition 3.1) using the method of Ahlfors and Bers (Ann. Math. 72(2):385–404, 1960). Then we use this proposition to choose good parameterization for our min-max sequences. We prove a compactification result (Lemma 4.1) similar to that of Colding and Minicozzi (Width and finite extinction time of Ricci flow, 0707.0108 [math.DG], 2007), and then give bubbling convergence results similar to that of Ding et al. (Invent. math. 165:225–242, 2006). In fact, we get an approximating result similar to the classical deformation lemma (Theorem 1.1).