Work

Huber Theorem Revisited in Dimension 4

Year: 2026

Type: article

Abstract: We study the second Huber theorem in dimension 4. Given a metric having a pointwise singularity with $$L^p$$ L p -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 $$\varepsilon $$ 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 $$W^{2,\frac{4}{3}+\varepsilon }$$ W 2 , 4 3 + ε .

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-026-02470-5

Authors: Paul Laurain, Dorian Martino

Institutions: Université Gustave Eiffel, ETH Zurich

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Eidgenössische Technische Hochschule Zürich