Infinitely many solutions for a boundary Yamabe problem

Luca Battaglia; Giusi Vaira; Yixing Pu

Infinitely many solutions for a boundary Yamabe problem

Analysis of PDEs 2025-06-30 v2 Differential Geometry

Authors: Luca Battaglia , Giusi Vaira , Yixing Pu

Abstract

We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature in the unit ball endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence of infinitely many non-radial positive solutions when the dimension is larger or equal to 5. This is the first result of existence of solutions in the case of negative prescribed scalar curvature problem in higher dimensions.

Keywords

yamabe problem boundary value problems differential geometry

Cite

@article{arxiv.2503.06192,
  title  = {Infinitely many solutions for a boundary Yamabe problem},
  author = {Luca Battaglia and Giusi Vaira and Yixing Pu},
  journal= {arXiv preprint arXiv:2503.06192},
  year   = {2025}
}