Conformal Mapping 2.0

Toby Driscoll

University of Delaware

Shortly after Riemann published his landmark existence theorem for conformal maps, many constructive methods for such maps emerged. Unfortunately, these methods require the knowledge of numbers or functions that are very difficult to compute by hand except in limited, simple circumstances. Thus conformal mapping remained a means for solving a few famous problems, or for making general statements. Today the situation is utterly different. Free software exists to compute conformal maps quickly in a wide variety of situations, and some classical but still-important problems can be solved in quite arbitrary geometry to as much accuracy as one could hope for. In the future we can expect the tools to become better integrated and more automatic, more easily applied to design and inverse problems, and to expand to include regions that are still difficult, such as those with high connectivity.

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