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

Thioglycolic acid on the gold (111) surface and Raman vibrational spectra

The interaction of thioglycolic acid with the Au(111) surface is investigaged, and it is found that at the low coverage the molecule lies down on the substrate. If the mercaptan-hydrogen atom is eliminated, the resulting SCH_2COOH molecule is randomly oriented on the surface. If the carboxylic acid group in the HSCH_2COOH molecule is deprotonated instead, the HSCH_2COO^ molecule lies down on the surface. However, when the mercaptan-hydrogen atom in the HSCH_2COO^- molecule is removed, the resulting SCH_2COO^- molecule rises up to a certain level on the substrate. The calculated Raman vibrational spectra decipher which compounds and atomic displacements contribute to the corresponding frequencies. We thus propose a consistent mechanism for the deposition of thioglycolic acid on the Au(111) surface.Comment: 18 pages, 5 figures, submitted to J. Chem. Phy