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The spectrum of the Laplace operator for a spherical space form

Gr. Tsagas (1983)

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

Si determina lo spettro di un operatore di Laplace di una «spherical space form» ( M , g ) e si studia l’influenza di tale spettro su ( M , g ) .

The super complex Frobenius theorem

C. Denson Hill, Santiago R. Simanca (1991)

Annales Polonici Mathematici

We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.

The topological complexity of sets of convex differentiable functions.

Mohammed Yahdi (1998)

Revista Matemática Complutense

Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.

The versality discriminant and local topological equivalence of mappings

James Damon (1990)

Annales de l'institut Fourier

We will extend the infinitesimal criteria for the equisingularity (i.e. topological triviality) of deformations f of germs of mappings f 0 : k s , 0 k t , 0 to non-finitely determined germs (these occur generically outside the “nice dimensions” for Mather, even among topologically stable mappings). The failure of finite determinacy is described geometrically by the “versality discriminant”, which is the set of points where f 0 is not stable (i.e. viewed as an unfolding it is not versal). The criterion asserts that...

Thom polynomials for open Whitney umbrellas of isotropic mappings

Toru Ohmoto (1996)

Banach Center Publications

A smooth mapping f : L n ( M 2 n , ω ) of a smooth n-dimensional manifold L into a smooth 2n-dimensional symplectic manifold (M,ω) is called isotropic if f*ω vanishes. In the last ten years, the local theory of singularities of isotropic mappings has been rapidly developed by Arnol’d, Givental’ and several authors, while it seems that the global theory of their singularities has not been well studied except for the work of Givental’ [G1] in the case of dimension 2 (cf. [A], [Au], [I2], [I-O]). In the present paper,...

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