On the structure of the family of extremal quasiconformal mappings of parabolic regions^*

^*Work done with support from NSF grant MC'S-8300248: University of Minnesota Mathemaric.; Report 83-164.

Abstract

The phenomenon of nonunique extremality of quasiconformal mappings with specified boundary values is studied by means of the known example with the boundary values . The concept of critical extremal mapping is introduced. By constructing an appropriate class of variations of A _k within the class of extremal mappings it is shown that A _k is a noncritical extremal for every s, 1 < s < 3. A critical extremal is explicitly identified when s= 2.

AMS (MOS):

• 30C70
• 30C60

^*Work done with support from NSF grant MC'S-8300248: University of Minnesota Mathemaric.; Report 83-164.

^*Work done with support from NSF grant MC'S-8300248: University of Minnesota Mathemaric.; Report 83-164.

Notes

^*Work done with support from NSF grant MC'S-8300248: University of Minnesota Mathemaric.; Report 83-164.