NON-EXISTENCE OF YAMABE MINIMIZERS ON SINGULAR SPHERES

Kazuo Akutagawa (1) , Ilaria Mondello (2)

1 Graduate School of Information Sciences [Sendaï]
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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]

Kazuo Akutagawa, Ilaria Mondello. NON-EXISTENCE OF YAMABE MINIMIZERS ON SINGULAR SPHERES. 2019. ⟨hal-02294751⟩