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Peer-reviewedCC BY 4.0Mathematics

Blow-Up Phenomena for a Boundary Yamabe Problem with Umbilic Boundary

  • Giusi Vaira1
  1. 1Dipartimento di Matematica, Universitá degli Studi di Bari Aldo Moro, 70125 Bari, Italy
Open at sourceDOICite

Abstract

We study a linear boundary perturbation of the problem of prescribing the scalar curvature K and the boundary mean curvature H on a Riemannian manifold with umbilic boundary. Assuming that the Weyl tensor is nowhere vanishing along the boundary, we treat separately the cases in which K and H are constant and non-constant. In the negative scalar-curvature regime K<0, and in dimensions n≥8, we prove the existence of positive solutions that blow up at the boundary as the perturbation parameter tends to zero.

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Cite

BibTeXRIS
BibTeX
@article{vaira2026blowup,
  title = {{Blow-Up Phenomena for a Boundary Yamabe Problem with Umbilic Boundary}},
  author = {Giusi Vaira},
  journal = {Mathematics},
  year = {2026},
  month = sep,
  doi = {10.3390/math14193555},
  url = {https://www.mdpi.com/2227-7390/14/19/3555},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Blow-Up Phenomena for a Boundary Yamabe Problem with Umbilic Boundary
AU  - Giusi Vaira
PY  - 2026
DA  - 2026/09/30
JO  - Mathematics
DO  - 10.3390/math14193555
UR  - https://www.mdpi.com/2227-7390/14/19/3555
AB  - We study a linear boundary perturbation of the problem of prescribing the scalar curvature K and the boundary mean curvature H on a Riemannian manifold with umbilic boundary. Assuming that the Weyl tensor is nowhere vanishing along the boundary, we treat separately the cases in which K and H are constant and non-constant. In the negative scalar-curvature regime K<0, and in dimensions n≥8, we prove the existence of positive solutions that blow up at the boundary as the perturbation parameter tends to zero.
SN  - 2227-7390
ER  -