A unified flow approach to smooth, even LpL_p-Minkowski problems

We study long-time existence and asymptotic behaviour for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of smooth, even $L_p$-Minkowski problems in $\mathbb{R}^{n+1}$ for $p>-n-1.$Comment: 21 pages. Comments are welcom

Effects of extended impurity perturbation in d-wave superconductor

We describe the effects of electronic perturbation distributed on nearest neighbor sites to the impurity center in a planar \textit{d}-wave superconductor, in approximation of circular Fermi surface. Alike the behavior previously reported for point-like perturbation and square Fermi surface, the quasiparticle density of states $\rho (\epsilon)$ can display a resonance inside the gap (and very weak features from low symmetry representations of non-local perturbation) and asymptotically vanishes at $\epsilon \to 0$ as $\rho\sim\epsilon/\ln^2\epsilon$. The local suppression of SC order parameter in this model is found to be somewhat weaker than for an equivalent point-like (non-magnetic) perturbation and much weaker than for a spin-dependent (extended) perturbation.Comment: 7 pages, 5 figures, some minor typos and the curves in Fig. 5 correcte