NON-EXISTENCE OF YAMABE MINIMIZERS ON SINGULAR SPHERES
Résumé
We prove that a minimizer of the Yamabe functional does not exist for a sphere S^n of dimension n ≥ 3, endowed with a standard edge-cone spherical metric of cone angle greater than or equal to 4π, along a great circle of codimension two. When the cone angle along the singularity is smaller than 2π, the corresponding metric is known to be a Yamabe metric, and we show that all Yamabe metrics in its conformal class are obtained from it by constant multiples and conformal diffeomorphisms preserving the singular set.
Domaines
Géométrie différentielle [math.DG]
Origine : Fichiers produits par l'(les) auteur(s)
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