Parallel Mean Curvature Surfaces in Symmetric Spaces

We present a reduction of codimension theorem for surfaces with parallel mean curvature in symmetric spaces

Surgery and the Spectrum of the Dirac Operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat

Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold

Suppose $M$ is a manifold with boundary. Choose a point $o\in\partial M$. We investigate the prescribed Ricci curvature equation \Ric(G)=T in a neighborhood of $o$ under natural boundary conditions. The unknown $G$ here is a Riemannian metric. The letter $T$ in the right-hand side denotes a (0,2)-tensor. Our main theorems address the questions of the existence and the uniqueness of solutions. We explain, among other things, how these theorems may be used to study rotationally symmetric metrics near the boundary of a solid torus $\mathcal T$. The paper concludes with a brief discussion of the Einstein equation on $\mathcal T$.Comment: 13 page

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Instantons and Killing spinors

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde

Measurement of the branching ratios of the Z0 into heavy quarks

We measure the hadronic branching ratios of the Z0 boson into heavy quarks: Rb=Gamma(Z0->bb)/Gamma(Z0->hadrons) and Rc=Gamma(Z0->cc/Gamma(Z0->hadrons) using a multi-tag technique. The measurement was performed using about 400,000 hadronic Z0 events recorded in the SLD experiment at SLAC between 1996 and 1998. The small and stable SLC beam spot and the CCD-based vertex detector were used to reconstruct bottom and charm hadron decay vertices with high efficiency and purity, which enables us to measure most efficiencies from data. We obtain, Rb=0.21604 +- 0.00098(stat.) +- 0.00073(syst.) -+ 0.00012(Rc) and, Rc= 0.1744 +- 0.0031(stat.) +- 0.0020(syst.) -+ 0.0006(Rb)Comment: 37 pages, 8 figures, to be submitted to Phys. Rev. D version 2: changed title to ratios, used common D production fractions for Rb and Rc and corrected Zgamma interference. Identical to PRD submissio

Direct Measurements of A_b and A_c using Vertex/Kaon Charge Tags at SLD

Exploiting the manipulation of the SLC electron-beam polarization, we present precise direct measurements of the parity violation parameters A_c and A_b in the Z boson - c quark and Z boson - b quark coupling. Quark/antiquark discrimination is accomplished via a unique algorithm that takes advantage of the precise SLD CCD vertex detector, employing the net charge of displaced vertices as well as the charge of kaons that emanate from those vertices. From the 1996-98 sample of 400,000 Z decays, produced with an average beam polarization of 73.4%, we find A_c = 0.673 +/- 0.029 (stat.) +/- 0.023 (syst.) and A_b = 0.919 +/- 0.018 (stat.) +/- 0.017 (syst.).Comment: 11 pages, 2 figures, 2 tables, to be submitted to Physical Review Letters; version 2 reflects changes suggested by the refere

Search for time-dependent B0s - B0s-bar oscillations using a vertex charge dipole technique

We report a search for B0s - B0s-bar oscillations using a sample of 400,000 hadronic Z0 decays collected by the SLD experiment. The analysis takes advantage of the electron beam polarization as well as information from the hemisphere opposite that of the reconstructed B decay to tag the B production flavor. The excellent resolution provided by the pixel CCD vertex detector is exploited to cleanly reconstruct both B and cascade D decay vertices, and tag the B decay flavor from the charge difference between them. We exclude the following values of the B0s - B0s-bar oscillation frequency: Delta m_s < 4.9 ps-1 and 7.9 < Delta m_s < 10.3 ps-1 at the 95% confidence level.Comment: 18 pages, 3 figures, replaced by version accepted for publication in Phys.Rev.D; results differ slightly from first versio

Causal structures and causal boundaries

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.Comment: Final version. To appear in Classical and Quantum Gravit