Mathematics – Complex Variables
Scientific paper
2007-04-16
J. Math. Anal. Appl. 360:561-576 (2009)
Mathematics
Complex Variables
22 pages, 4 figures Changes in v2: Changed some definitions and exchanged ordering of theorems for clarity purposes. Typos cor
Scientific paper
We obtain a first order differential equation for the driving function of the chordal Loewner differential equation in the case where the domain is slit by a curve which is a trajectory arc of certain quadratic differentials. In particular this includes the case when the curve is a path on the square, triangle or hexagonal lattice in the upper halfplane or, indeed, in any domain with boundary on the lattice. We also demonstrate how we use this to calculate the driving function numerically. Equivalent results for other variants of the Loewner differential equation are also obtained: Multiple slits in the chordal Loewner differential equation and the radial Loewner differential equation. The method also works for other versions of the Loewner differential equation. The proof of our formula uses a generalization of Schwarz-Christoffel mapping to domains bounded by trajectory arcs of rotations of a given quadratic differential that is of interest in its own right.
No associations
LandOfFree
The Loewner driving function of trajectory arcs of quadratic differentials 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 The Loewner driving function of trajectory arcs of quadratic differentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Loewner driving function of trajectory arcs of quadratic differentials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-44029