Università degli studi di Padova, Italia
Date(s) : 26/03/2018 iCal
14 h 30 min - 15 h 30 min
Let E be a compact non-pluripolar subset of R^n. The Baran metric delta_E on the interior of E is a Finsler metric that is defined by means of certain directional derivatives of the plurisubharmonic extremal function V*_E of E as subset of C^n. We consider some examples where delta_E turns out to be a Riemannian metric. We show that in this cases the eigenfunctions of the Laplace Beltrami operator are the orthonormal polynomials with respect to the pluripotential equilibrium measure of E. This may be regarded as a multidimensional generalization of the property of Chebyshev polynomials of being eigenfunction of a Sturm Liouville problem. Finally, we try to put such a result in the framework of the so called compatible complexification of compact Riemannian manifolds and entire Grauert tubes.