TL;DR
This paper discusses Conway's theory of quilts to construct transplantable pairs of plane domains that are isospectral for the Laplace operator, highlighting a method for generating such pairs.
Contribution
It introduces numerous new transplantable pairs based on Conway's quilt theory, expanding the known methods for creating isospectral domains.
Findings
Multiple new transplantable pairs constructed
Demonstrates the effectiveness of quilt theory in isospectral domain creation
Provides a framework for further exploration of isospectral geometries
Abstract
A `transplantable pair' is a pair of glueing diagrams that can be used to create pairs of plane domains that are isospectral for the Laplace operator. We present a host of transplantable pairs worked out by John Conway using his theory of quilts
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Taxonomy
TopicsMathematics and Applications · Advanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation