Potential theory and applications in conformal geometry

2025/12/05 by Ma, Shiguang, Qing, Jie · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2512.06188

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.

Citations

• p-Laplace equations in conformal geometry
• Linear potentials and applications in conformal geometry
• On Huber's type theorems in general dimensions
• On n-superharmonic functions and some geometric applications
• Hypersurfaces with nonnegative Ricci curvature in hyperbolic space
• Fractional conformal Laplacians and fractional Yamabe problems
• Spectral characterization of Poincaré-Einstein manifolds with infinity of positive Yamabe type
• The ambient metric
• On positive solutions to semi-linear conformally invariant equations on locally conformally flat manifolds
• Compactness for conformal metrics with Constant Q curvature on locally conformally flat manifolds
• Scattering Matrix in Conformal Geometry
• The Wiener test and potential estimates for quasilinear elliptic equations
• Conformally flat manifolds, Kleinian groups and scalar curvature

Cited by

• On potentials for sub-Laplacians and geometric applications

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• Linear potentials and applications in conformal geometry
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