Mathematics – Complex Variables
Scientific paper
2008-11-16
Mathematics
Complex Variables
32 pages
Scientific paper
Consider the straightening phi of a Beltrami form that is constant on a square, with the corresponding ellipses having a vertical major axis, and null outside. A generalized Schwarz-Christoffel formula is used to express the inverse of phi. The formula is found by introducing an affine Riemann surface. This formula is used to draw on a computer the image of the square by phi, and practical aspects are discussed. The resulting shapes are shown for different values of the constant dilatation ratio of the ellipses (=major axis/minor axis). The limit when this ratio tends to infinity is surprising. A model of this limit is proposed, produced by an affine surface uniformization.
No associations
LandOfFree
Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening 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 Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-466281