Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions.
Zayed, E.M.E. (1997)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “A method of symmetrization ; Applications to heat and spectral estimates”
Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions.
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In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of isoperimetric profile. The main point is to connect the decay of the norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods....
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