Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome

Minimal graphic functions on manifolds of non-negative Ricci curvature

We study minimal graphic functions on complete Riemannian manifolds \Si with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with such growth via splitting for tangent cones of \Si at infinity. When, in contrast, we do not impose any growth restrictions for minimal graphic functions, we also obtain a Liouville type theorem under a certain non-radial Ricci curvature decay condition on \Si. In particular, the borderline for the Ricci curvature decay is sharp by our example in the last section.Comment: 38 page

Superconducting gap symmetry of Ba0.6K0.4Fe2As2 studied by angle-resolved photoemission spectroscopy

We have performed high-resolution angle-resolved photoemission spectroscopy on the optimally-doped Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ compound and determined the accurate momentum dependence of the superconducting (SC) gap in four Fermi-surface sheets including a newly discovered outer electron pocket at the M point. The SC gap on this pocket is nearly isotropic and its magnitude is comparable ($\Delta$ $\sim$ 11 meV) to that of the inner electron and hole pockets ($\sim$12 meV), although it is substantially larger than that of the outer hole pocket ($\sim$6 meV). The Fermi-surface dependence of the SC gap value is basically consistent with $\Delta$($k$) = $\Delta$$_0$cos$k_x$cos$k_y$ formula expected for the extended s-wave symmetry. The observed finite deviation from the simple formula suggests the importance of multi-orbital effects.Comment: 4 pages, 3 figures, 1 tabl

Single crystal growth and physical properties of SrFe2_{2}(As1−x_{1-x}Px_{x})2_{2}

We report a crystal growth and physical properties of SrFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$. The single crystals for various $x$s were grown by a self flux method. For $x = 0.35$, $T_c$ reaches the maximum value of 30\,K and the electrical resistivity $\rho$($T$) shows $T$-linear dependence. As $x$ increases, $T_{c}$ decreases and $\rho$($T$) changes to $T^2$-behavior, indicating a standard Fermi liquid. These results suggest that a magnetic quantum critical point exists around $x=0.35$.Comment: 4 pages, 4 figures, accepted to Supplemental issue of the Journal of Physical Society of Japan (JPSJ