The Nirenberg problem and its generalizations: a unified approach
type: Item
instance of: scholarly article
title: The Nirenberg problem and its generalizations: a unified approach
zbMATH Open document ID: 1384.53039
author: Tianling Jin
author: Jingang Xiong
author: Yan Yan Li
published in: Mathematische Annalen
publication date: 2017-09-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.5743
review text: The authors aim to develop a unified approach to establish blow-up profiles, compactness and existence of positive solutions of the conformally invariant equations \(P_{\sigma }(v)=K\upsilon ^{\frac{n+2\sigma }{n-2\sigma }}\) on the standard unit sphere \(\mathbb{S}^{n}\) for all \(\sigma \in (0,n/2)\), using integral representations. When \(\sigma =1\), it is the prescribing scalar curvature problem or the Nirenberg problem, and when \(\sigma =2\), it is the prescribing \(Q\)-curvature problem.
reviewed by: Cihan Özgür
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 45M20
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 6780248
zbMATH Keywords: Nirenberg problem
zbMATH Keywords: \(Q\)-curvature problem
MaRDI profile type: Publication
OpenAlex ID: W2129507212
arXiv ID: 1411.5743
cites work: A complete study of the lack of compactness and existence results of a fractional Nirenberg equation via a flatness hypothesis. I
cites work: The scalar-curvature problem on the standard three-dimensional sphere
cites work: \(Q\)-curvature flow on 4-manifolds
cites work: Prescribed \(Q\)-curvature on manifolds of even dimension
cites work: Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
cites work: Scalar Curvature Functions in a Conformal Class of Metrics and Conformal Transformations
cites work: Sharp Inequalities, the Functional Determinant, and the Complementary Series
cites work: Prescribing a higher order conformal invariant on \(S^n\)
cites work: Global existence and convergence for a higher order flow in conformal geometry
cites work: Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities
cites work: An Extension Problem Related to the Fractional Laplacian
cites work: On fractional GJMS operators
cites work: Fractional Laplacian in conformal geometry
cites work: The scalar curvature equation on 2- and 3-spheres
cites work: An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
cites work: A perturbation result for prescribing mean curvature
cites work: Prescribing Gaussian curvature on S 2
cites work: Conformal deformations of metric on \({\mathcal S}\) 2
cites work: Extremal metrics of zeta function determinants on 4-manifolds
cites work: Existence results for the fractional Nirenberg problem
cites work: Classification of solutions for an integral equation
cites work: \(Q\)-curvature flow on the standard sphere of even dimension
cites work: Indefinite fractional elliptic problem and Liouville theorems
cites work: Paneitz-type operators and applications
cites work: Existence of conformal metrics with constant \(Q\)-curvature
cites work: PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT
cites work: Q5699170
cites work: The prescribed boundary mean curvature problem on \(\mathbb B^4\)
cites work: Conformal metrics with prescribed mean curvature on the boundary
cites work: Conformal metrics on the ball with zero scalar curvature and prescribed mean curvature on the boundary
cites work: Conformal metrics with prescribed scalar curvature
cites work: Mountain pass critical points for Paneitz-Branson operators.
cites work: On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
cites work: Q3738176
cites work: Juhl’s formulae for GJMS operators and $Q$-curvatures
cites work: Existence of conformal metrics on \(S^ n\) with prescribed fourth-order invariant.
cites work: Singular solutions of fractional order conformal Laplacians
cites work: Fractional conformal Laplacians and fractional Yamabe problems
cites work: Conformally Invariant Powers of the Laplacian, I: Existence
cites work: Scattering matrix in conformal geometry
cites work: A strong maximum principle for the Paneitz operator and a non-local flow for the \(\mathcal Q\)-curvature
cites work: Prescribing Gaussian curvature on \(S^ 2\)
cites work: The Yamabe problem on manifolds with boundary: Existence and compactness results
cites work: \(Q\) curvature on a class of 3-manifolds
cites work: Q-Curvature on a Class of Manifolds with Dimension at Least 5
cites work: Sign of Green's Function of Paneitz Operators and theQCurvature
cites work: Asymptotic analysis for fourth order Paneitz equations with critical growth
cites work: COMPACTNESS AND GLOBAL ESTIMATES FOR A FOURTH ORDER EQUATION OF CRITICAL SOBOLEV GROWTH ARISING FROM CONFORMAL GEOMETRY
cites work: Prescribed \(Q\)-curvature flow on \(S^n\)
cites work: Results of prescribing \(Q\)-curvature on \(S^{n}\)
cites work: On a Fractional Nirenberg Problem, Part II: Existence of Solutions
cites work: A fractional Yamabe flow and some applications
cites work: Sharp constants in weighted trace inequalities on Riemannian manifolds
cites work: On the recursive structure of Branson's \(Q\)-curvatures
cites work: Explicit formulas for GJMS-operators and \(Q\)-curvatures
cites work: Gaussian curvature and conformal mapping
cites work: The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\)
cites work: Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Remark on some conformally invariant integral equations: the method of moving spheres

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Compactness of conformal metrics with constant \(Q\)-curvature. I

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: \(Q\)-curvature flow on \(S^4\)

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Q5184115

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Constant \(Q\)-curvature metrics in arbitrary dimension

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: On positive solutions to semilinear conformally invariant equations on locally conformally flat manifolds

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Compactness for conformal metrics with constant \(Q\) curvature on locally conformally flat manifolds

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Positive solutions for a fourth order equation invariant under isometries

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Admissible $Q-$curvatures under isometries for the conformal GJMS operators

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Prescribed scalar curvature on the \(n\)-sphere

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: On conformal deformations of metrics on \(S^n\)

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Prescribing \(Q\)-curvature problem on \(S^n\)

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Uniqueness theorem for integral equations and its application

The Nirenberg problem and its generalizations: a unified approach (cites work)
cites work: Prescribing integral curvature equation.

The Nirenberg problem and its generalizations: a unified approach (DOI)
DOI: 10.1007/S00208-016-1477-Z

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