Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary

DOI10.1016/j.anihpc.2021.01.005zbMath1475.35050arXiv1906.01317OpenAlexW3131334292MaRDI QIDQ2235190

Seunghyeok Kim, Monica Musso, Wei, Juncheng

Publication date: 20 October 2021

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.01317

zbMATH Keywords

positive mass theoremblow-up analysisboundary Yamabe problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) PDEs on manifolds (35R01) Conformal structures on manifolds (53C18) Differential geometry of submanifolds of Möbius space (53A31)

Related Items (4)

Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with umbilic boundary ⋮ A compactness theorem for the fractional Yamabe problem. I: The nonumbilic conformal infinity ⋮ Blowing-up solutions for supercritical Yamabe problems on manifolds with umbilic boundary ⋮ Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary

Cites Work

• Unnamed Item
• Unnamed Item
• A positive mass theorem for asymptotically flat manifolds with a non-compact boundary
• Compactness and non-compactness for the Yamabe problem on manifolds with boundary
• A compactness theorem for scalar-flat metrics on manifolds with boundary
• An existence theorem of conformal scalar-flat metrics on manifolds with boundary
• Blow-up phenomena for scalar-flat metrics on manifolds with boundary
• The prescribed boundary mean curvature problem on \(\mathbb B^4\)
• Problèmes de Neumann non linéaires sur les variétés riemanniennes
• A geometric equation with critical nonlinearity on the boundary
• Compactness of solutions to the Yamabe problem. III
• A compactness theorem for the Yamabe problem
• Blow-up phenomena for the Yamabe equation. II
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• The Yamabe problem on manifolds with boundary
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• Prescribing scalar and boundary mean curvature on the three dimensional half sphere
• Linear perturbation of the Yamabe problem on manifolds with boundary
• Barycenter technique and the Riemann mapping problem of Cherrier-Escobar
• Compactness of conformal metrics with constant \(Q\)-curvature. I
• Blow-up phenomena for linearly perturbed Yamabe problem on manifolds with umbilic boundary
• Conformal metrics with prescribed mean curvature on the boundary
• Uniqueness theorems through the method of moving spheres
• The Yamabe problem on manifolds with boundary: Existence and compactness results
• An existence theorem for the Yamabe problem on manifolds with boundary
• Linear perturbations of the fractional Yamabe problem on the minimal conformal infinity
• A compactness theorem for the fractional Yamabe problem. I: The nonumbilic conformal infinity
• Compactness for conformal scalar-flat metrics on umbilic boundary manifolds
• Uniqueness of solutions of the Yamabe problem on manifolds with boundary
• A compactness theorem on Branson's \(Q\)-curvature equation
• A compactness theorem for scalar-flat metrics on 3-manifolds with boundary
• Existence theorems of the fractional Yamabe problem
• Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary
• A priori estimates for the Yamabe problem in the non-locally conformally flat case
• Compactness of solutions to the Yamabe problem. II
• Nondegeneracy of the bubble in the critical case for nonlocal equations
• Blow-up phenomena for the Yamabe equation
• Uniqueness theorems on conformal deformation of metrics, sobolev inequalities, and an eigenvalue estimate
• Existence results for the Yamabe problem on manifolds with boundary
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• Convergence of the Yamabe flow on manifolds with minimal boundary

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