On nonisometric isospectral connected fractal domains.

Sleeman, Brian D., and Hua, Chen. "On nonisometric isospectral connected fractal domains.." Revista Matemática Iberoamericana 16.2 (2000): 351-361. <http://eudml.org/doc/39604>.

@article{Sleeman2000,
abstract = {A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries and by following a technique of paper folding maps by J. Chapman 1993 we construct pairs of isospectral but non-isometric connected planar domains with fractal boundaries having the same Minkowski dimension.},
author = {Sleeman, Brian D., Hua, Chen},
journal = {Revista Matemática Iberoamericana},
keywords = {Variedad riemanniana; Isometría; Dominios; Fractales; Variedades compactas; Isoespectralidad; fractal boundary; Riemannian manifolds; isospectral; spectrum; Dirichlet Laplacians},
language = {eng},
number = {2},
pages = {351-361},
title = {On nonisometric isospectral connected fractal domains.},
url = {http://eudml.org/doc/39604},
volume = {16},
year = {2000},
}

TY - JOUR
AU - Sleeman, Brian D.
AU - Hua, Chen
TI - On nonisometric isospectral connected fractal domains.
JO - Revista Matemática Iberoamericana
PY - 2000
VL - 16
IS - 2
SP - 351
EP - 361
AB - A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries and by following a technique of paper folding maps by J. Chapman 1993 we construct pairs of isospectral but non-isometric connected planar domains with fractal boundaries having the same Minkowski dimension.
LA - eng
KW - Variedad riemanniana; Isometría; Dominios; Fractales; Variedades compactas; Isoespectralidad; fractal boundary; Riemannian manifolds; isospectral; spectrum; Dirichlet Laplacians
UR - http://eudml.org/doc/39604
ER -