How Long to Read Old and New Aspects in Spectral Geometry

How Long Does it Take to Read Old and New Aspects in Spectral Geometry?

It takes the average reader 7 hours and 39 minutes to read Old and New Aspects in Spectral Geometry by M.-E. Craioveanu

Assuming a reading speed of 250 words per minute. Learn more

Description

It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.

How long is Old and New Aspects in Spectral Geometry?

Old and New Aspects in Spectral Geometry by M.-E. Craioveanu is 447 pages long, and a total of 114,879 words.

This makes it 151% the length of the average book. It also has 140% more words than the average book.

How Long Does it Take to Read Old and New Aspects in Spectral Geometry Aloud?

The average oral reading speed is 183 words per minute. This means it takes 10 hours and 27 minutes to read Old and New Aspects in Spectral Geometry aloud.

What Reading Level is Old and New Aspects in Spectral Geometry?

Old and New Aspects in Spectral Geometry is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Old and New Aspects in Spectral Geometry?

Old and New Aspects in Spectral Geometry by M.-E. Craioveanu is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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