Some uniformization problems for a fourth order conformal curvature

Global Riemannian geometry, including pinching (53C20) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Conformal structures on manifolds (53C18)

Cites Work

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The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\)
Deformations of \(Q\)-curvature. I
An upper bound of the total Q-curvature and its isoperimetric deficit for higher-dimensional conformal Euclidean metrics
Constant t-curvature conformal metrics on 4-manifolds with boundary
Conformal metrics with constant \(Q\)-curvature for manifolds with boundary
The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds
The Yamabe problem on manifolds with boundary
The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics
The zeta functional determinants on manifolds with boundary. I: The formula
The zeta functional determinants on manifolds with boundary. II: Extremal metrics and compactness of isospectral set
On the Chern-Gauss-Bonnet integral for conformal metrics on \(\mathbb{R}^4\)
Compactness properties for geometric fourth order elliptic equations with application to the \(Q\)-curvature flow
Uniqueness and non-existence theorems for conformally invariant equations
A formal Riemannian structure on conformal classes and uniqueness for the \(\sigma_2\)-Yamabe problem
An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
Extremal metrics of zeta function determinants on 4-manifolds
The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE
Integrability of scalar curvature and normal metric on conformally flat manifolds
Deformations of \(Q\)-curvature. II.
The isoperimetric inequality and \(Q\)-curvature
Existence of conformal metrics with constant \(Q\)-curvature
The Nirenberg problem and its generalizations: a unified approach
Prescribed \(Q\)-curvature problem on closed 4-Riemannian manifolds in the null case
Riemannian manifolds with positive Yamabe invariant and Paneitz operator
Lectures on the fourth-order \(Q\) curvature equation
The Isoperimetric Inequality and Quasiconformal Maps on Manifolds with Finite Total Q-curvature
Explicit Functional Determinants in Four Dimensions
Compactness of solutions to some geometric fourth-order equations
Integral pinching results for manifolds with boundary
Regularity of weak solutions to critical exponent variational equations
The sharp type Chern-Gauss-Bonnet integral and asymptotic behavior
The total Q-curvature, volume entropy and polynomial growth polyharmonic functions

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