Locally nearly spherical surfaces are almost-positively cc-curved

The $c$-curvature of a complete surface with Gauss curvature close to 1 in $C^2$ norm is almost-positive (in the sense of Kim--McCann). Our proof goes by a careful case by case analysis combined with perturbation arguments from the constant curvature case, keeping track of an estimate on the closeness curvature condition

Hyperbolic Alexandrov-Fenchel quermassintegral inequalities I

In this paper we prove the following geometric inequality in the hyperbolic space \H^n ($n\ge 5)$, which is a hyperbolic Alexandrov-Fenchel inequality, \begin{array}{rcl} \ds \int_\Sigma \s_4 d \mu\ge \ds\vs C_{n-1}^4\omega_{n-1}\left\{\left(\frac{|\Sigma|}{\omega_{n-1}} \right)^\frac 12 + \left(\frac{|\Sigma|}{\omega_{n-1}} \right)^{\frac 12\frac {n-5}{n-1}} \right\}^2, \end{array} provided that $\Sigma$ is a horospherical convex hypersurface. Equality holds if and only if $\Sigma$ is a geodesic sphere in \H^n.Comment: 18page

A new mass for asymptotically flat manifolds

In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay order $\tau$ satisfies $\tau > \frac {n-4}{3}.$ Then we show a positive mass theorem for asymptotically flat graphs over ${\mathbb R}^n$. Moreover we obtain also Penrose type inequalities in this case.Comment: 32 pages. arXiv:1211.7305 was integrated into this new version as an applicatio

The Gauss-Bonnet-Chern mass of conformally flat manifolds

In this paper we show positive mass theorems and Penrose type inequalities for the Gauss-Bonnet-Chern mass, which was introduced recently in \cite{GWW}, for asymptotically flat CF manifolds and its rigidity.Comment: 17 pages, references added, the statement of Prop. 4.6 correcte

Human Resource Flow and Software Firm Performance: The Role of Direct vs. Indirect Competitors

Recent years have witnessed increasingly stiff competition for talents among software firms. The economic impact of obtaining workers from or losing workers to competing firms, however, has rarely been quantified. Built on the literature of human resource flow and firm competition, this study examines the impact of human resource flows from and to different types of competitors on company performance. In particular, we divide competitors into direct and indirect competitors according to their market and resource similarity. Using a large dataset on labour mobility derived from LinkedIn.com, we quantify the impact of employees who came from or joined direct and indirect competitors respectively. We find that employees from competitors bring great benefits to the recipient firms. Specifically, a 1 percent increase of the number of employees from direct (indirect) competitors that join the focal company in the previous year increases the company’s economic value added by 0.054 (0.074) percent in the current year. Our results also contribute to the existing literature on human resources and company strategy and provide practical implications to recruiters and policy makers in the software industry

Study on the structure and properties of new metallocene high branched polyethylene

The branching composition, distribution and melting crystallization properties of very low density polyethylenes (VLDPE) with different carbon chain length were studied by means of nuclear magnetic resonance (NMR) and differential scanning calorimetry (DSC). The average sequence length (nE, nH, nB), relative monomer distribution (RMD) and monomer reactivity ratio (rE, rH, rB) were selected to analyze the polymerization characteristics. The crystallization characteristics of wafer thickness (L), relative branching degree (S) and crystallinity (Xc) were discussed by means of SSA thermal classification method. It has been found that the comonomer content and branching degree of VLDPE products with hexene (C6) as co monomers is lower than that of butene (C4) copolymer products; while the crystallinity and lamellar thickness is higher than that of C4 products