A Class of Fully Nonlinear Equations Arising in Conformal Geometry
Li Chen, Xi Guo, Yan He
Abstract
Abstract In this paper, we consider the equations of Krylov type in conformal geometry on closed smooth Riemannian manifolds, which can be viewed as an extension of $\sigma _k$-Yamabe equation. Moreover, we prove local gradient and 2nd-derivative estimates for solutions to these equations and establish an existence result.
Topics & Concepts
MathematicsConformal mapConformal geometryNonlinear systemClass (philosophy)Extension (predicate logic)Riemannian geometryMathematical analysisGeometryPure mathematicsConformal symmetryPhysicsComputer scienceArtificial intelligenceProgramming languageQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringGeometric Analysis and Curvature Flows