Micalyn Rowe, Texas A&M University – Commerce

Analysis on the Intersection of Two Disks

Abstract: Many problems in STEM require working in regions with inconvenient geometries. Special types of complex functions, called conformal mappings, make these problems easier to work on. In this project, we work on a domain, which is the area of intersection between two disks. We first create a conformal mapping which maps  to the unit disk. Then, we explore some integrability properties of different derivative orders of the conformal map on. We prove that if the angle of intersection divides , then the conformal map is smooth on an open set containing  and if the angle of intersection is less than , the integral of the squared modulus of the -order derivative of the conformal map is finite on  (This work is a collaboration with Cristo R. Sanchez.)

Presentation Author(s):
Micalyn Rowe*, Cristo Sanchez

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