Title

A Nonlinear Differential Inequality and Counterexamples for Holder Continuous Almost Complex Structures

Document Type

Presentation

Presentation Date

12-1-2009

Conference Name

Analysis Seminar

Conference Location

University of Wisconsin - Madison

Peer Review

Invited

Abstract

We consider a second order quasilinear partial differential inequality 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, 0<\alpha<1, and f(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, generalizing an example of Ivashkovich, Pinchuk, and Rosay.

Disciplines

Analysis | Mathematics

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