Optimal regularity of minimal graphs in the hyperbolic space

We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the H\"older exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.Comment: Accepted by Calc. Var. Partial Differential Equation

Blow-up sets of Ricci curvatures of complete conformal metrics

A version of the singular Yamabe problem in smooth domains in a closed manifold yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study the blow-up phenomena of Ricci curvatures of these metrics on domains whose boundary is close to a certain limit set of a lower dimension. We will characterize the blow-up set according to the Yamabe invariant of the underlying manifold. In particular, we will prove that all points in the lower dimension part of the limit set belong to the blow-up set on manifolds not conformally equivalent to the standard sphere and that all but one point in the lower dimension part of the limit set belong to the blow-up set on manifolds conformally equivalent to the standard sphere. In certain cases, the blow-up set can be the entire manifold. We will demonstrate by examples that these results are optimal

In vitro and in vivo double-enhanced suicide gene therapy mediated by generation 5 polyamidoamine dendrimers for PC-3 cell line

<p>Abstract</p> <p>Background</p> <p>One of the most frequently used and efficient suicide gene therapies for prostate cancer is HSV-TK/GCV system, but its application has been limited due to lack of favorable gene vector and the reduction of "bystander effect". We investigated the effect of a novel combination of HSV-TK/GCV fused with Cx43 and gemcitabine using non-viral vector generation 5 polyamidoamine dendrimers (G5-PAMAM-D) on PC-3 cells.</p> <p>Methods</p> <p>RT-PCR and Western blot were used to detect TK and Cx43 expression. Cell viability and proliferation were measured by using MTT assay. Cell apoptosis was detected with double-staining of Annexin V-FITC and propidium iodide (PI) by flow cytometry. Nude mice models were established to evaluate the therapeutic effect in vivo.</p> <p>Results</p> <p>G5-PAMAM-D efficiently delivered recombinant plasmids into PC-3 cells and HSV-TK and Cx43 could be expressed successfully. With gemcitabine, G5-PAMAM-D mediated HSV-TK and Cx43 expression effectively inhibited prostate cancer PC-3 cell proliferation, leading to more cellular apoptosis and inhibiting PC-3 tumor growth in nude mice models.</p> <p>Conclusions</p> <p>This study illustrates that this new suicide gene system mediated by G5-PAMAM-D is effective in decreasing PC-3 cell proliferation and inducing cell apoptosis, and inhibiting tumor growth in vivo. In a word, our study could provide a potential approach for gene therapy of prostate cancer.</p