13, October at 19:00 MSK
The classical Sobolev inequality is considered on non-compact, complete, connected Riemannian manifolds. The geometry of a manifold is described in terms of isoperimetric inequalities. Provided that the manifold is p-hyperbolic, the Sobolev inequality is established, which depends on the geometry of the manifold. An example of a symmetric manifold is given, on which p -hyperbolicity can be easily verified. Further, we discuss possible applications in studying the properties of solutions of equations on manifolds.
D.Sc. A.F. Tedeev (Leading scientific researcher of Southern Mathematical Institute of the VSC of RAS, Vladikavkaz, Russian Federation).
Title of the talk: The Sobolev inequality on Riemannian manifolds.