Geodesic
Isospectrality and Galois projective geometries
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 660-664

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We construct a series of pairs of domains in the plane and pairs of surfaces with boundary that are isospectral but not isometric. The construction is based on the existence of finite transformation groups that are spectrally equivalent but not isomorphic. 
@article{MZM_1998_63_5_a2,
     author = {Ya. B. Vorobets and A. M. Stepin},
     title = {Isospectrality and {Galois} projective geometries},
     journal = {Matemati\v{c}eskie zametki},
     pages = {660--664},
     publisher = {mathdoc},
     volume = {63},
     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a2/}
}
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Ya. B. Vorobets; A. M. Stepin. Isospectrality and Galois projective geometries. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 660-664. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a2/