NON-EXISTENCE OF YAMABE MINIMIZERS ON SINGULAR SPHERES

Abstract : 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.
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Submitted on : Monday, September 23, 2019 - 4:21:46 PM
Last modification on : Friday, October 4, 2019 - 1:37:38 AM

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

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