Counterexamples to Upper Semicontinuity of the Kobayashi-Royden Pseudonorm for Rough Almost Complex Structures
Southeastern Sectional Meeting of the American Mathematical Society
University of Kentucky
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
Adam Coffman and Yifei Pan (2010).
Counterexamples to Upper Semicontinuity of the Kobayashi-Royden Pseudonorm for Rough Almost Complex Structures. Presented at Southeastern Sectional Meeting of the American Mathematical Society, University of Kentucky.