Interior curvature estimates for hypersurfaces of prescribing scalar curvature in dimension three
Guohuan Qiu
Abstract
abstract: We prove a priori interior curvature estimates for hypersurfaces of prescribing scalar curvature equations in $\mathbb{R}^{3}$. The method is motivated by the integral method of Warren and Yuan. The new observation here is that we construct a ``Lagrangian'' graph which is a submanifold of bounded mean curvature if the graph function of a hypersurface satisfies a scalar curvature equation.
Topics & Concepts
Scalar curvatureMathematicsCurvaturePrescribed scalar curvature problemDimension (graph theory)Sectional curvatureMathematical analysisScalar (mathematics)Mean curvatureGeometryPure mathematicsGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchGeometry and complex manifolds