Constant \(Q\)-curvature metrics on conic 4-manifolds

DOI10.1515/acv-2019-0056zbMath1501.53042arXiv1907.03409OpenAlexW3044945464MaRDI QIDQ2119567

Yanyan Li

Publication date: 29 March 2022

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.03409

zbMATH Keywords

conic manifolds\(Q\)-curvature

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) PDEs on manifolds (35R01) Conformal structures on manifolds (53C18)

Related Items

\(\sigma_2\) Yamabe problem on conic 4-spheres, Singular metrics of constant negative \(Q\)-curvature in Euclidean spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Prescribing the \(Q\)-curvature on the sphere with conical singularities
• On convergence to a football
• Sharp singular Adams inequalities in high order Sobolev spaces
• The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\)
• Prescribed \(Q\)-curvature on manifolds of even dimension
• A sharp inequality of J. Moser for higher order derivatives
• Symmetry and related properties via the maximum principle
• Estimates and extremals for zeta function determinants on four-manifolds
• On the structure of spaces with Ricci curvature bounded below. I
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Global existence and convergence for a higher order flow in conformal geometry
• Extremal metrics of zeta function determinants on 4-manifolds
• What kinds of singular surfaces can admit constant curvature?
• Lower bounds on Ricci curvature and the almost rigidity of warped products
• Adams' inequality and limiting Sobolev embeddings into Zygmund spaces
• The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE
• The \(\operatorname{SU}(3)\) Toda system with multiple singular sources
• The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds
• Existence of conformal metrics with constant \(Q\)-curvature
• \(\sigma_2\) Yamabe problem on conic 4-spheres
• Constant \(Q\)-curvature metrics in arbitrary dimension
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Conformally Invariant Powers of the Laplacian, I: Existence
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• The Yamabe problem
• Explicit Functional Determinants in Four Dimensions
• Liouville Equation and Spherical Convex Polytopes
• K‐Stability and Kähler‐Einstein Metrics
• Compactness of solutions to some geometric fourth-order equations
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof