One cannot hear the shape of a drum
微分几何
2008-02-03 v1
摘要
We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, ``can one hear the shape of a drum?'' In order to construct simply connected examples, we exploit the observation that an orbifold whose underlying space is a simply connected manifold with boundary need not be simply connected as an orbifold.
引用
@article{arxiv.math/9207215,
title = {One cannot hear the shape of a drum},
author = {Carolyn Gordon and David L. Webb and Scott Wolpert},
journal= {arXiv preprint arXiv:math/9207215},
year = {2008}
}
备注
5 pages