Number and location of pre-images under harmonic mappings in the plane
Number and location of pre-images under harmonic mappings in the plane
We derive a formula for the number of pre-images under a non-degenerate harmonic mapping $f$, using the argument principle. This formula reveals a connection between the pre-images and the caustics. Our results allow to deduce the number of pre-images under $f$ geometrically for every non-caustic point. We approximately locate the …