Extension to a classical theorem of Liouville and applications
by
Yanyan Li
Rutgers University

The classical Liouville theorem says that a positive entire harmonic function must be constant. We give a fully nonlinear version of it. This extension enables us to establish optimal local gradient estimates of solutions to general conformally invariant fully nonlinear elliptic equations of second order. This talk will start from a new proof of the classical Liouville theorem using only the comparison principle and the invariance of harmonicity under Mobius transformations. We will then outline the proof of the comparison principle used in establishing the new Liouville theorem. Finally we outline the proof of the gradient estimates via the Liouville theorem.

Date received: July 18, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavl-51.