Critical metrics for log-determinant functionals in conformal geometry

DOI10.4310/jdg/1707767336arXiv1906.08188MaRDI QIDQ6200609

Pierpaolo Esposito, Andrea Malchiodi

Publication date: 22 March 2024

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.08188

zbMATH Keywords

quantization property elliptic equations of Liouville type functionals on compact four-dimensional manifolds Polyakov’s formula

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Fundamental solutions to PDEs (35A08) Nonlinear higher-order PDEs (35G20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Variational methods for higher-order elliptic equations (35J35) Blow-up in context of PDEs (35B44)

Cites Work

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Non-uniqueness results for critical metrics of regularized determinants in four dimensions
Topological degree for solutions of fourth order mean field equations
Extremal metrics for spectral functions of Dirac operators in even and odd dimensions
Singular solutions of the $p$-Laplace equation
The existence of surfaces of constant mean curvature with free boundaries
Compact isospectral sets of surfaces
Extremals of determinants of Laplacians
A sharp inequality of J. Moser for higher order derivatives
Prescribing Gaussian curvatures on surfaces with conical singularities
Estimates and extremals for zeta function determinants on four-manifolds
Best constant in Sobolev inequality
Problèmes isoperimetriques et espaces de Sobolev
Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics
On a sharp Sobolev-type inequality on two-dimensional compact manifolds
Existence results for mean field equations
Sharp borderline Sobolev inequalities on compact Riemannian manifolds
Inverting the $p$-harmonic operator
Uniqueness of the functional determinant
Nonlinear elliptic systems with measure-valued right hand side
The differential equation $\Delta u=8\pi-8\pi he^u$ on a compact Riemann surface
A classification result for the quasi-linear Liouville equation
Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory
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
On a quasilinear mean field equation with an exponential nonlinearity
$p$-harmonic tensors and quasiregular mappings
Existence of conformal metrics with constant $Q$-curvature
Local behavior of solutions of quasi-linear equations
Concentration phenomena for Liouville's equation in dimension four
Isolated singularities of solutions of quasi-linear equations
R-torsion and the Laplacian on Riemannian manifolds
Isospectral Conformal Metrics on 3-Manifolds
Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition
Explicit Functional Determinants in Four Dimensions
Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
Nonlinear Elliptic Equations with Right Hand Side Measures
Regularity of a Fourth Order Nonlinear PDE with Critical Exponent
Weak minima of variational integrals.
Asymptotic behavior of a nonlinear fourth order eigenvalue problem
Sharp estimates for solutions of multi‐bubbles in compact Riemann surfaces
Uniqueness and maximal regularity for nonlinear elliptic systems of n--Laplace type with measure valued right hand side
Quantization effects for a fourth-order equation of exponential growth in dimension $4$
Compactness of solutions to some geometric fourth-order equations
Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth
Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
Regularity of weak solutions to critical exponent variational equations
Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems

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