Potential theory and applications in conformal geometry

Authors

  • Shiguang Ma
  • Jie Qing

DOI:

https://doi.org/10.1285/i15900932v45s1p147

Keywords:

Riesz potentials, Wolff potentials, capacities, thin sets, scalar curvature equations, $Q$-curvature equations, $p$-Laplace equations, Huber's type theorems, Hausdorff dimensions

Abstract

In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal geometry. We establish the asymptotic behavior near singularities and derive applications in conformal geometry. In particular, we establish some Huber's type theorems and Hausdorff dimension estimates of the ends in conformal geometry in general dimensions.

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Published

20-01-2026

Issue

Volume 45, suppl. 1 (2025)

Section

Articoli

License

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode