Topological and differentiable rigidity of submanifolds in space forms

Let $F^{n+p}(c)$ be an $(n+p)$-dimensional simply connected space form with nonnegative constant curvature $c$. We prove that if $M^n(n\geq4)$ is a compact submanifold in $F^{n+p}(c)$, and if $Ric_M>(n-2)(c+H^2),$ where $H$ is the mean curvature of $M$, then $M$ is homeomorphic to a sphere. We also show that the pinching condition above is sharp. Moreover, we obtain a new differentiable sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page

The sphere theorems for manifolds with positive scalar curvature

Some new differentiable sphere theorems are obtained via the Ricci flow and stable currents. We prove that if $M^n$ is a compact manifold whose normalized scalar curvature and sectional curvature satisfy the pointwise pinching condition $R_0>\sigma_{n}K_{\max}$, where $\sigma_n\in (\frac{1}{4},1)$ is an explicit positive constant, then $M$ is diffeomorphic to a spherical space form. This gives a partial answer to Yau's conjecture on pinching theorem. Moreover, we prove that if $M^n(n\geq3)$ is a compact manifold whose $(n-2)$-th Ricci curvature and normalized scalar curvature satisfy the pointwise condition $Ric^{(n-2)}_{\min}>\tau_n(n-2)R_0,$ where $\tau_n\in (\frac{1}{4},1)$ is an explicit positive constant, then $M$ is diffeomorphic to a spherical space form. We then extend the sphere theorems above to submanifolds in a Riemannian manifold. Finally we give a classification of submanifolds with weakly pinched curvatures, which improves the differentiable pinching theorems due to Andrews, Baker and the authors.Comment: 35 page

Clinical analysis of buried optic nerve drusen with optical coherence tomography examination

AIM: To explore the specific image of buried optic nerve drusen during optical coherence tomography(OCT)examination. <p>METHODS: A retrospective study was made on 6 patients with buried optic nerve drusen(6 eyes)diagnosed by fundus fluorescein angiography(FFA)and B scan examination. <p>RESULTS: The high fluorescence area of optic disc showed on the FFA image of all 6 patients imaged with the spectral OCT revealed cluster of calcium deposits. These deposits demonstrated specific wide bars with high reflectivity casting shadows underneath and had lacunae appearance. <p>CONCLUSION: Buried optic nerve drusen showed specific image in the spectral OCT examination. Thus, spectral OCT can serve as an assistant examination method with relatively prominent features for diagnosing buried optic nerve drusen. It can help to raise the detection rate of buried optic nerve drusen

Measurement of Mercury in Flue Gas Based on an Aluminum Matrix Sorbent

The measurement of total mercury in flue gas based on an economical aluminum matrix sorbent was developed in this paper. A sorbent trap consisted of three tubes was employed to capture Hg from flue gas. Hg trapped on sorbent was transferred into solution by acid leaching and then detected by CVAAS. Hg adsorbed on sorbent was recovered completely by leaching process. The 87.7% recovery of Hg in flue gas by tube 1 and tube 2 was obtained on the equipment of coal combustion and sampling in lab. In order to evaluate the ability to recover and accurately quantify Hg0 on the sorbent media, the analytical bias test on tube 3 spiked with Hg0 was also performed and got the average recovery of 97.1%. Mercury measurements based on this method were conducted for three coal-fired power plants in China. The mercury in coal is distributed into bottom ash, electrostatic precipitator (ESP) ash, wet flue gas desulfurization (WFGD) reactant, and flue gas, and the relative distribution varied depending on factors such as the coal type and the operation conditions of plants. The mercury mass balances of three plants were also calculated which were 91.6%, 77.1%, and 118%, respectively. The reliability of this method was verified by the Ontario Hydro (OH) method either in lab or in field