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# Preshears of Rosette Mappings

Jerrell Cockerham ’21
Major: Mathematics

Jerrell Cockerham ’21

Major: Mathematics

Faculty Collaborator: Jane McDougall, Mathematics & Computer Science

We explore properties of the preshears of rosette harmonic mappings. These mappings were discovered by generalizing the harmonic mapping in the form of a$6$-noded rosette that was obtained as the conformal mapping onto a symmetric cross. We consider the preshears for each integer $n$ with $n\geq3.$ By construction, the preshear conformal mappings have exterior angles at vertices that are $\pm\pi/2$ or $\pi,$ and the image regions consist of $n-3$block-shaped regions. We note that the shear construction fails due to the non CRA nature of both the rosette images and of the conformal mapping.