Seminar “Some remarks on the Sobolev inequality in Riemannian manifolds”

25 May at 19:30 MSK

We investigate Sobolev  and Hardy inequalities, specifically weighted Minerbe’s  type estimates, in non compact  completeconnected Riemannian manifolds whose geometry is described by an isoperimetric profile. In particular, we assume that the manifold satisfies the p-hyperbolicity property, stated in terms of a necessary integral Dini condition on the isoperimetric profile. Our method seems to us to combine sharply the knowledge of the isoperimetric profile and the optimal Bliss type Hardy inequality depending on the geometry of the manifold. We recover the well known best  Sobolev constant in the Euclidean case( results of joint investigations with professor Daniele Andreucci).

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