Counterexamples to Upper Semicontinuity of the Kobayashi-Royden Pseudonorm for Rough Almost Complex Structures

Document Type


Presentation Date

Spring 3-27-2010

Conference Name

Southeastern Sectional Meeting of the American Mathematical Society

Conference Location

University of Kentucky

Peer Review



For each alpha in (0,1), we construct a manifold with an alpha-Holder continuous almost complex structure, such that the Kobayashi-Royden pseudonorm is not upper semicontinuous. This generalizes an example due to Ivashkovich, Pinchuk, and Rosay, with alpha = 1/2. The main idea in the construction is an analysis of complex valued functions f on the unit disk satisfying df/dzbar=|f|^alpha.


Analysis | Geometry and Topology | Mathematics