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UID:7344@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180326T143000
DTEND;TZID=Europe/Paris:20180326T153000
DTSTAMP:20241120T203919Z
URL:https://www.i2m.univ-amu.fr/evenements/riemannian-structures-surfacing
 -from-pluripotential-theory-some-examples/
SUMMARY:Federico Piazzon (Università degli studi di Padova\, Italia): Riem
 annian structures surfacing from pluripotential theory: some examples
DESCRIPTION:Federico Piazzon: 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 plurisubhar
 monic extremal function V*_E of E as subset of C^n. We consider some examp
 les where delta_E turns out to be a Riemannian metric. We show that in thi
 s cases the eigenfunctions of the Laplace Beltrami operator are the orthon
 ormal polynomials with respect to the pluripotential equilibrium measure o
 f E. This may be regarded as a multidimensional generalization of the prop
 erty 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 ent
 ire Grauert tubes. \n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/03/Federico_Piazzon.jpg
CATEGORIES:Séminaire,Analyse et Géométrie
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DTSTART:20180325T030000
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