A notion of the weighted \(\sigma_{k}\)-curvature for manifolds with density

DOI10.1016/j.aim.2016.03.010zbMath1337.53047arXiv1409.4455OpenAlexW284825795WikidataQ125368505 ScholiaQ125368505MaRDI QIDQ271732

Jeffrey S. Case

Publication date: 20 April 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4455

zbMATH Keywords

smooth metric measure space\(\mathcal{W}\)-functionalgradient Ricci solitonmanifold with densityweighted \(\sigma_k\)-curvature

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Critical metrics (58E11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

The weighted \(\sigma_k\)-curvature of a smooth metric measure space ⋮ On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow ⋮ Convergence rate of the weighted Yamabe flow ⋮ Weighted Yamabe solitons ⋮ Rigidity of weighted Einstein smooth metric measure spaces ⋮ Some integral formulae on weighted manifolds ⋮ Generalized Hsiung-Minkowski formulae on manifolds with density ⋮ The weighted ambient metric ⋮ A weighted renormalized curvature for manifolds with density

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Addendum to ``Perelman's reduced volume and a gap theorem for the Ricci flow
• On second variation of Perelman's Ricci shrinker entropy
• On complete gradient shrinking Ricci solitons
• Remarks on non-compact gradient Ricci solitons
• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• Perelman's reduced volume and a gap theorem for the Ricci flow
• Comparison geometry for the Bakry-Emery Ricci tensor
• Removability of singularities for a class of fully nonlinear elliptic equations
• A Yamabe-type problem on smooth metric measure spaces
• Variational status of a class of fully nonlinear curvature prescription problems
• Sharp logarithmic Sobolev inequalities on gradient solitons and applications
• Extended obstruction tensors and renormalized volume coefficients
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• On the structure of manifolds with positive scalar curvature
• Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein
• Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators
• The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics
• Some geometric properties of the Bakry-Émery-Ricci tensor
• Entropy and reduced distance for Ricci expanders
• Three-manifolds with positive Ricci curvature
• An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
• Geometric inequalities on locally conformally flat manifolds
• A conformally invariant sphere theorem in four dimensions
• Smooth metric measure spaces, quasi-Einstein metrics, and tractors
• Conformal geometry, contact geometry, and the calculus of variations
• The Yamabe problem for higher order curvatures
• The conjectures on conformal transformations of Riemannian manifolds
• A note on renormalized volume functionals
• Eigenvalues of the drifted Laplacian on complete metric measure spaces
• On a fully nonlinear Yamabe problem
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• A Class of Variational Functionals in Conformal Geometry
• The Yamabe problem
• On some conformally invariant fully nonlinear equations
• Conformally invariant Monge-Ampère equations: Global solutions
• Some properties of the Schouten tensor and applications to conformal geometry
• A weighted renormalized curvature for manifolds with density
• A new variational characterization of three-dimensional space forms

This page was built for publication: A notion of the weighted \(\sigma_{k}\)-curvature for manifolds with density