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Pré-Publication, Document De Travail Année : 2021

Non-existence of Yamabe minimizers on singular spheres

Kazuo Akutagawa
  • Fonction : Auteur

Résumé

We prove that a minimizer of the Yamabe functional does not exist for a sphere $\mathbb{S}^n$ of dimension $n \geq 3$, endowed with a standard edge-cone spherical metric of cone angle greater than or equal to $4\pi$, along a great circle of codimension two. When the cone angle along the singularity is smaller than $2\pi$, 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.

Dates et versions

hal-03147250 , version 1 (19-02-2021)

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Citer

Kazuo Akutagawa, Ilaria Mondello. Non-existence of Yamabe minimizers on singular spheres. 2021. ⟨hal-03147250⟩
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