France-Italy meeting in Geometric Analysis

Geometric rigidity of constant heat flow

speaker: Alessandro Savo (Sapienza Università di Roma)

abstract: On a compact Riemannian manifold with boundary we consider the solution u=u(t,x) of the heat equation with constant unit initial data and Dirichlet boundary conditions. If at every fixed time t the normal derivative of u(t,.) is a constant function on the boundary, we say that the manifold has the "constant flow property". In this talk we discuss the geometry of manifolds having the constant flow property and we give a classification result which shows that this property is an analytic counterpart of the isoparametric property, very much studied in Riemannian geometry. We also relate the constant flow property with other overdetermined problems, in particular, the classical Serrin problem on the mean-exit time function.

timetable:
Fri 24 Feb, 9:00 - 10:00, Aula Dini
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