Title

Some Nonlinear Differential Inequalities and an Application to Hölder Continuous Almost Complex Structures

Document Type

Article

Publication Date

2011

Publication Source

Annales de l'Institut Henri Poincare (C) Non Linear Analysis

Volume

28

Issue

2

Inclusive pages

149-157

Peer Reviewed

yes

Abstract

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.

Keywords

Differential inequality, Almost complex manifold

Disciplines

Analysis | Geometry and Topology | Mathematics

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Link to Original Published Item

http://dx.doi.org/10.1016/j.anihpc.2011.02.001