Some Problems Regarding the Spectra of Hodge-de Rham Operators » książka
Some Problems Regarding the Spectra of Hodge-de Rham Operators
ISBN-13: 9783838348162 / Angielski / Miękka / 2010 / 140 str.
Spectral geometry deals with the survey of these natural, differential operators' spectrums and among other things it tries to emphasize geometrical and topological properties of a manifold that can be recuperated from the spectrums. The present work is going to approach several issues referring to the spectrums of Hodge-de Rham operators on closed Riemannian manifolds. The author of this paper is going to discuss the continuous dependence on the Riemannian metrics on a smooth and closed differential manifold of the eigenvalues of the Hodge-de Rham operators and its restrictions regarding the exact, differential form spaces and consequences of such feature. Moreover, by using J. Wenzelburger's idea 80], 81], we are going to prove that the eigenvalues of the Hodge-de Rham operators even smoothly depend on the Riemannian metrics on a smooth, closed, differential manifold if the Frechet smooth manifold canonical structure is taken into consideration in the space of all Riemannian metrics with such a manifold."
Spectral geometry deals with the survey of these natural, differential operators spectrums and among other things it tries to emphasize geometrical and topological properties of a manifold that can be recuperated from the spectrums. The present work is going to approach several issues referring to the spectrums of Hodge-de Rham operators on closed Riemannian manifolds. The author of this paper is going to discuss the continuous dependence on the Riemannian metrics on a smooth and closed differential manifold of the eigenvalues of the Hodge-de Rham operators and its restrictions regarding the exact, differential form spaces and consequences of such feature. Moreover, by using J. Wenzelburgers idea [80], [81], we are going to prove that the eigenvalues of the Hodge-de Rham operators even smoothly depend on the Riemannian metrics on a smooth, closed, differential manifold if the Fréchet smooth manifold canonical structure is taken into consideration in the space of all Riemannian metrics with such a manifold.
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