Blow-up phenomena for the Yamabe equation

DOI10.1090/S0894-0347-07-00575-9zbMath1206.53041arXiv0905.3840OpenAlexW2482307565WikidataQ56672826 ScholiaQ56672826MaRDI QIDQ3058258

Simon Brendle

Publication date: 19 November 2010

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3840

zbMATH Keywords

scalar curvature Yamabe equation conformal deformation of Riemannian metrics, blow-up analysis

Mathematics Subject Classification ID

Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).

Related Items (97)

The second best constant for the Hardy-Sobolev inequality on manifolds ⋮ Blowing up solutions for supercritical Yamabe problems on manifolds with non-umbilic boundary ⋮ A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity ⋮ Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds ⋮ W1,p-metrics and conformal metrics with Ln/2-bounded scalar curvature ⋮ Conformal scalar curvature equation on Sn: Functions with two close critical points (Twin Pseudo-Peaks) ⋮ Linear perturbation of the Yamabe problem on manifolds with boundary ⋮ A Harnack-Type Inequality for a Prescribed-Curvature Equation on a Domain with Boundary ⋮ Multipeak solutions for the Yamabe equation ⋮ Compactness of solutions to nonlocal elliptic equations ⋮ Multiplicity of nodal solutions to the Yamabe problem ⋮ Existence theorems of the fractional Yamabe problem ⋮ The Calabi metric and desingularization of Einstein orbifolds ⋮ A non-compactness result on the fractional Yamabe problem in large dimensions ⋮ Asymptotic behavior of solutions to the $\sigma_{k}$-Yamabe equation near isolated singularities ⋮ Infinitely many blowing-up solutions for Yamabe-type problems on manifolds with boundary ⋮ Compactness for a class of Yamabe-type problems on manifolds with boundary ⋮ Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds ⋮ Multiplicity of solutions to the Yamabe equation on warped products ⋮ Infinitely many solutions for cubic nonlinear Schrödinger equations in dimension four ⋮ Construction of blow-up sequences for the prescribed scalar curvature equation on $S^n$. III: Aggregated and towering blow-ups ⋮ Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric ⋮ Bubble tree convergence for conformal metrics with $\int_M | R |^{\frac{n}{2}}\, d V_g$ bounds ⋮ Evolution equations in Riemannian geometry ⋮ Clustered solutions to low-order perturbations of fractional Yamabe equations ⋮ Nonuniqueness for a fully nonlinear boundary Yamabe-type problem via bifurcation theory ⋮ A generic result on Weyl tensor ⋮ Non-compactness of the prescribed $Q$-curvature problem in large dimensions ⋮ Construction of blow-up sequences for the prescribed scalar curvature equation on $S^n$. II: Annular domains ⋮ Refined estimates for simple blow-ups of the scalar curvature equation on $S^n$ ⋮ Non-compactness and infinite number of conformal initial data sets in high dimensions ⋮ A construction of constant scalar curvature manifolds with Delaunay-type ends ⋮ Invariant solutions of the Yamabe equation on the Koiso-Cao soliton ⋮ Equivariant solutions to the optimal partition problem for the prescribed $Q$-curvature equation ⋮ Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation ⋮ Deformations of the hemisphere that increase scalar curvature ⋮ Perturbative techniques in conformal geometry ⋮ Blow-up phenomena for scalar-flat metrics on manifolds with boundary ⋮ The effect of linear perturbations on the Yamabe problem ⋮ The existence of Hamiltonian stationary Lagrangian tori in Kähler manifolds of any dimension ⋮ Multiplicity results for the Yamabe equation by Lusternik-Schnirelmann theory ⋮ A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound ⋮ Multi-bump analysis for Trudinger-Moser nonlinearities I. Quantification and location of concentration points ⋮ Large outlying stable constant mean curvature spheres in initial data sets ⋮ Compactness of conformal metrics with constant $Q$-curvature. I ⋮ An efficient collocation method for a class of boundary value problems arising in mathematical physics and geometry ⋮ CONSTRUCTION OF BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON Sⁿ I: UNIFORM CANCELLATION ⋮ Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary ⋮ Convergence of the Yamabe flow in dimension 6 and higher ⋮ Uniformization theorems: between Yamabe and Paneitz ⋮ Generic properties of critical points of the Weyl tensor ⋮ Compactness and non-compactness for the Yamabe problem on manifolds with boundary ⋮ Positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five ⋮ Control of error in the homotopy analysis of semi-linear elliptic boundary value problems ⋮ Metrics of constant scalar curvature conformal to Riemannian products ⋮ Factorization into $k$-bubbles for Palais-Smale maps to potential type energy functionals ⋮ Blowing-up solutions for the Yamabe equation ⋮ A compactness theorem for scalar-flat metrics on manifolds with boundary ⋮ Compactness and non-compactness for Yamabe-type problems ⋮ A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture ⋮ Some results about the existence of critical points for the Willmore functional ⋮ Towering phenomena for the Yamabe equation on symmetric manifolds ⋮ An existence theorem for the Yamabe problem on manifolds with boundary ⋮ EXISTENCE ANDA PRIORIBOUNDS FOR ELECTROSTATIC KLEIN–GORDON–MAXWELL SYSTEMS IN FULLY INHOMOGENEOUS SPACES ⋮ A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_2$-Yamabe problem ⋮ A pointwise finite-dimensional reduction method for a fully coupled system of Einstein–Lichnerowicz type ⋮ Stationary Kirchhoff systems in closed high dimensional manifolds ⋮ Critical metrics on connected sums of Einstein four-manifolds ⋮ A compactness theorem for the fractional Yamabe problem. I: The nonumbilic conformal infinity ⋮ A fully nonlinear partial differential equation and its application to the $\sigma_k$-Yamabe problem ⋮ Stability of the Einstein-Lichnerowicz constraint system ⋮ The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds ⋮ Solutions of the Yamabe equation by Lyapunov-Schmidt reduction ⋮ Efficient low-error analytical-numerical approximations for radial solutions of nonlinear Laplace equations ⋮ Prescribing curvatures on three dimensional Riemannian manifolds with boundaries ⋮ Low energy nodal solutions to the Yamabe equation ⋮ A compactness theorem on Branson's $Q$-curvature equation ⋮ Blowing-up solutions for supercritical Yamabe problems on manifolds with umbilic boundary ⋮ Recent results on stationary critical Kirchhoff systems in closed manifolds ⋮ A compactness theorem for scalar-flat metrics on 3-manifolds with boundary ⋮ Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions $n \geq 7$ ⋮ Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary ⋮ A note on the uniqueness of solutions for the Yamabe problem ⋮ Stability and instability results for sign-changing solutions to second-order critical elliptic equations ⋮ Blow-up examples for the Yamabe problem ⋮ Bounded stability for strongly coupled critical elliptic systems below the geometric threshold of the conformal Laplacian ⋮ The Yamabe invariant ⋮ Sign-Changing Blow-Up for Scalar Curvature Type Equations ⋮ Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds ⋮ Sign-changing blow-up for the Yamabe equation at the lowest energy level ⋮ Yamabe problem in the presence of singular Riemannian foliations ⋮ Quantitative stability for minimizing Yamabe metrics ⋮ Blowing-up solutions to Bopp-Podolsky-Schrödinger-Proca and Schrödinger-Poisson-Proca systems in the electro-magneto-static case ⋮ A detailed proof of a theorem of Aubin ⋮ Gluing Eguchi‐Hanson Metrics and a Question of Page

Cites Work

This page was built for publication: Blow-up phenomena for the Yamabe equation