Search

It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R1³ is called of mixed type if it changes causal type from space-like to time-like. In R1³, Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes. [ABSTRACT FROM AUTHOR]

We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of complete minimal surfaces that includes algebraic minimal surfaces. It also provides a new proof of Fujimoto's theorem for this class, which not only simplifies the proof but also reveals the geometric meaning behind it. [ABSTRACT FROM AUTHOR]

Btk plays crucial roles in the differentiation and activation of B and myeloid cells. Despite drastic reductions of other Ig isotypes, paradoxically high IgE responses have been known in btk mutant mice. Here we show that btk-/- dendritic cells exhibit a more mature phenotype and a stronger in vitro and in vivo T cell- stimulatory ability than wild-type cells. Increased IgE responses were induced by adoptive transfer of btk-/- dendritic cells into mice. Consistent with the stronger T cell-stimulatory ability of btk-/- dendritic cells, btk-/- mice exhibited enhanced inflammation in Th2-driven asthma and Th1-driven contact sensitivity experiments. These negative regulatory functions of Btk in dendritic cells appear to be mediated mainly through autocrine secretion of IL-10 and subsequent activation of Stat3. [ABSTRACT FROM AUTHOR]