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

Intelligent enhancement of ancient Chinese murals based on multi-scale parallel structure

Ancient mural artwork preserves the historical background and cultural customs of that time through intricate details and bright colors. However, after the natural environment and man-made damage, these works of art are damaged in color, texture and content and lose their quality. In order to identify and enhance murals with large areas of color damage, we propose a multi-scale parallel GAN and parallel Unet structure, which can extract features from multiple scales or images to adapt to the changing scale of the target and provide a more diverse set of features. This structure can reduce the risk of overfitting the training data by learning more general features. The verification results of indicators such as PSNR on the ancient mural data set show that the method has a certain performance improvement effect