Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem

Details Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem

2007-08-29

arxiv.org/abs/0708.4001v1

J. London Math. Soc. 77 No. 1, 183-202, 2008

Mathematics

Complex Variables

21 pages

Scientific paper

We establish an extension of Liouville's classical representation theorem for solutions of the partial differential equation $\Delta u=4 e^{2u}$ and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps with prescribed critical points and specified boundary behaviour. For instance, we show that for every Blaschke sequence $\{z_j\}$ in the unit disk there is always a Blaschke product with $\{z_j\}$ as its set of critical points. Our work is closely related to the Berger-Nirenberg problem in differential geometry.

Affiliated with

Also associated with

No associations

Rating

Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-240745