Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Corro - Juan Carlos Fernández - R. Perales

Yamabe problem in the presence of singular Riemannian Foliations

created by corro on 31 Mar 2022



Inserted: 31 mar 2022
Last Updated: 31 mar 2022

Year: 2022

ArXiv: 2202.13109 PDF


Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-changing solutions to Yamabe type problems, which are constant along the leaves of the foliation, and one positive solution of minimal energy among any other solution with these symmetries. In particular, we find sign-changing solutions to the Yamabe problem on the round sphere with new qualitative behavior when compared to previous results, that is, these solutions are constant along the leaves of a singular Riemannian foliation which is not induced neither by a group action nor by an isoparametric function. To prove the existence of these solutions, we prove a Sobolev embedding theorem for general singular Riemannian foliations, and a Principle of Symmetric Criticality for the associated energy functional to a Yamabe type problem.

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