Abstract
Several years ago, motivated in part by the challenging problem of studying the scattering of light from “fractal” surfaces, the physicist Michael V. Berry formulated a very intriguing conjecture about the vibrations of “drums with fractal boundary”. Extending to the “fractal” case a long standing conjecture of Hermann Weyl, he conjectured in particular that the high frequencies of such “fractal drums” were governed by the Hausdorff dimension of their boundary [1,2].
Research partially supported by the National Science Foundation under Grant DMS-8703138.
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Lapidus, M.L. (1991). Can One Hear the Shape of a Fractal Drum? Partial Resolution of the Weyl-Berry Conjecture. In: Concus, P., Finn, R., Hoffman, D.A. (eds) Geometric Analysis and Computer Graphics. Mathematical Sciences Research Institute Publications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9711-3_13
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