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Peer-reviewedCC BYJournal of geometric analysis

Huber Theorem Revisited in Dimension 4.

  • Paul Laurain1
  • Dorian Martino2
  1. 1Departement de Mathématiques, Université Gustave Eiffel, Paris, France.
  2. 2Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland.
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Abstract

We study the second Huber theorem in dimension 4. Given a metric having a pointwise singularity with Lp -bounds on the Bach tensor, we construct a conformal metric which is regular across the singularity. To do so, we introduce another Coulomb-type condition, similar to the case of Yang-Mills connections. This enables us to obtain a conformal metric satisfying an ε -regularity property. We obtain a generalization of the two-dimensional case that can be applied to study the singularities of Bach-flat metrics and immersions with second fundamental forms in W2,43+ε .

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Cite

BibTeXRIS
BibTeX
@article{laurain2026huber,
  title = {{Huber Theorem Revisited in Dimension 4.}},
  author = {Paul Laurain and Dorian Martino},
  journal = {Journal of geometric analysis},
  year = {2026},
  month = may,
  doi = {10.1007/s12220-026-02470-5},
  url = {https://europepmc.org/article/MED/42922990},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Huber Theorem Revisited in Dimension 4.
AU  - Paul Laurain
AU  - Dorian Martino
PY  - 2026
DA  - 2026/05/22
JO  - Journal of geometric analysis
DO  - 10.1007/s12220-026-02470-5
UR  - https://europepmc.org/article/MED/42922990
AB  - We study the second Huber theorem in dimension 4. Given a metric having a pointwise singularity with Lp -bounds on the Bach tensor, we construct a conformal metric which is regular across the singularity. To do so, we introduce another Coulomb-type condition, similar to the case of Yang-Mills connections. This enables us to obtain a conformal metric satisfying an ε -regularity property. We obtain a generalization of the two-dimensional case that can be applied to study the singularities of Bach-flat metrics and immersions with second fundamental forms in W2,43+ε .
SN  - 1050-6926
SN  - 1559-002X
ER  -