%0 Journal Article
%T Some nonlinear differential inequalities and an application to H£żlder continuous almost complex structures
%A Adam Coffman
%A Yifei Pan
%J Mathematics
%D 2009
%I arXiv
%X We consider some second order quasilinear partial differential inequalities for real valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at the origin. As a consequence, for complex valued functions $f(z)$ satisfying $\partial f/\partial\bar z=|f|^\alpha$, $0<\alpha<1$, and $f(0)\ne0$, there is also a lower bound for $\sup|f|$ on the unit disk. For each $\alpha$, we construct a manifold with an $\alpha$-H\"older continuous almost complex structure where the Kobayashi-Royden pseudonorm is not upper semicontinuous.
%U http://arxiv.org/abs/0907.3307v1