Conformal deformation on manifolds with boundary

DOI10.1007/s00039-009-0028-0zbMath1185.53042arXiv0811.2521OpenAlexW2068067097MaRDI QIDQ2655445

Szu-Yu Sophie Chen

Publication date: 25 January 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.2521

zbMATH Keywords

manifold with boundaryGauss-Bonnet formulafully nonlinear equationsconformal invariantYamabe constant

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (19)

Compactness of conformally compact Einstein manifolds in dimension 4 ⋮ The Neumann problem for a type of fully nonlinear complex equations ⋮ The \(k\)-Yamabe solitons and the quotient Yamabe solitons ⋮ On the prescribed boundary mean curvature problem via local Pohozaev identities ⋮ On the \(\sigma_2\)-curvature and volume of compact manifolds ⋮ Nonuniqueness for a fully nonlinear boundary Yamabe-type problem via bifurcation theory ⋮ Renormalized area for minimal hypersurfaces of 5D Poincaré-Einstein spaces ⋮ Conformal rigidity of the hemispheres \({{\text S}^4_+}\) and \({{\text S}^6_+}\) ⋮ A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary ⋮ Conformally variational Riemannian invariants ⋮ The Neumann problem for Hessian equations ⋮ From Optimal Transportation to Conformal Geometry ⋮ Chern-Gauss-Bonnet formula for singular Yamabe metrics in dimension four ⋮ Nonuniqueness for a fully nonlinear, degenerate elliptic boundary-value problem in conformal geometry ⋮ Boundary operators associated to the \(\sigma_{k}\)-curvature ⋮ A Dirichlet's principle for the \(k\)-Hessian ⋮ Prescribing the symmetric function of the eigenvalues of the Schouten tensor ⋮ Some rigidity properties for manifolds with constant \(k\)-curvature of modified Schouten tensor ⋮ A positive energy theorem for fourth-order gravity

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