A compactness theorem on Branson's \(Q\)-curvature equation

DOI10.2140/pjm.2019.302.119zbMath1434.53041arXiv1505.07692OpenAlexW416984750WikidataQ126829189 ScholiaQ126829189MaRDI QIDQ2305367

Gang Li

Publication date: 10 March 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.07692

zbMATH Keywords

maximum principlecompactnesspositive mass theoremfourth-order elliptic equationsblowup argumentconstant \(Q\)-curvature metrics

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Semilinear elliptic equations (35J61)

Related Items

A note on prescribed Q-curvature, A non-compactness result on the fractional Yamabe problem in large dimensions, Compactness of conformal metrics with constant \(Q\)-curvature. I, Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary, A compactness theorem for the fractional Yamabe problem. I: The nonumbilic conformal infinity, The effect of pinching conditions in prescribing \(Q\)-curvature on standard spheres

Cites Work

• Unnamed Item
• Unnamed Item
• A strong maximum principle for the Paneitz operator and a non-local flow for the \(\mathcal Q\)-curvature
• Compactness of solutions to the Yamabe problem. III
• The Paneitz equation in hyperbolic space
• A compactness theorem for the Yamabe problem
• Blow-up phenomena for the Yamabe equation. II
• Positive mass theorem for the Paneitz-Branson operator
• On the proof of the positive mass conjecture in general relativity
• Estimate of the conformal scalar curvature equation via the method of moving planes. II
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Mountain pass critical points for Paneitz-Branson operators.
• A new proof of the positive energy theorem.
• Paneitz-type operators and applications
• Compactness of conformal metrics with constant \(Q\)-curvature. I
• Prescribed scalar curvature on the \(n\)-sphere
• Nonuniqueness and high energy solutions for a conformally invariant scalar equation
• Non-compactness of the prescribed \(Q\)-curvature problem in large dimensions
• The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
• Nonlinear biharmonic equations with negative exponents
• The Nirenberg problem and its generalizations: a unified approach
• Compactness for conformal metrics with constant \(Q\) curvature on locally conformally flat manifolds
• A priori estimates for the Yamabe problem in the non-locally conformally flat case
• Compactness of solutions to the Yamabe problem. II
• The spacetime positive mass theorem in dimensions less than eight
• Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator
• QCurvature on a Class of 3-Manifolds
• Blow-up phenomena for the Yamabe equation
• Q-Curvature on a Class of Manifolds with Dimension at Least 5
• On positive solutions to semilinear conformally invariant equations on locally conformally flat manifolds
• Differential operators cononically associated to a conformal structure.
• The Yamabe problem
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• Compactness and global estimates for the geometric Paneitz equation in high dimensions
• A Polyharmonic Generalization of a Theorem on Harmonic Functions