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On isometries of the symmetric space P₁(3,ℝ)

Gašper Zadnik (2014)

Colloquium Mathematicae

We classify the isometries in the non-identity component of the whole isometry group of the symmetric space of positive 3 × 3 matrices of determinant 1: we determine the translation lengths, minimal spaces and fixed points at infinity.

On nonisometric isospectral connected fractal domains.

Brian D. Sleeman, Chen Hua (2000)

Revista Matemática Iberoamericana

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...

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