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Abstract

We will introduce conditions which are sufficient to guarantee that a closed connected domain in R^2 that has a smooth boundary does not have a nice complementary set of rays.

Author Bio

Ever since the fifth grade when I learned about exponents, I've wanted to bea mathematician. I had excellent math teachers all through middle schooland high school, who inspired me to want to know more. I just loved mathand couldn't get enough of it. I'm still that same way but I've moved pastthe simplicity of exponents into studying differential geometry. I graduated from Brigham Young University with my Bachelor of Science degreein Mathematics. I'm currently finishing my Master of Science degree in Mathas well with an emphasis in differential geometry. While an undergrad, Iwrote this paper while working with Denise Halverson on some questions aboutnetwork paths in the hyperbolic plane. We took a tangent and startedworking with non-convex domains in the Euclidean plane. I conjectured andproved a statement about connected non-convex domains with smooth boundaryand wrote this paper. Since that time, I've continued to work with Dr.Halverson as one of my Thesis committee members.

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