Some Nonlinear Differential Inequalities and an Application to Hölder Continuous Almost Complex Structures
Annales de l'Institut Henri Poincare (C) Non Linear Analysis
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 df/dzbar=|f|^alpha, 0f(0) not =0, there is also a lower bound for sup|f| on the unit disk. For each alpha, we construct a manifold with an alpha-Holder continuous almost complex structure where the Kobayashi-Royden pseudonorm is not upper semicontinuous.
Differential inequality, Almost complex manifold
Analysis | Geometry and Topology | Mathematics
Adam Coffman and Yifei Pan (2011).
Some Nonlinear Differential Inequalities and an Application to Hölder Continuous Almost Complex Structures. Annales de l'Institut Henri Poincare (C) Non Linear Analysis.28 (2), 149-157.