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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...

On non-Uniqueness of Complex Geodesies in Convex Bounded Domains

Graziano Gentili (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di in un dominio convesso limitato D di uno spazio di Banach complesso E , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di D .

On normal CR-submanifolds of S-manifolds

José Cabrerizo, Luis Fernández, Manuel Fernández (1993)

Colloquium Mathematicae

Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for...

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