Sobolev Inequalities in Manifolds with Nonnegative Curvature

Simon Brendle

2022Communications on Pure and Applied Mathematics58 citationsDOI

Abstract

Abstract We prove a sharp Sobolev inequality on manifolds with nonnegative Ricci curvature. Moreover, we prove a Michael‐Simon inequality for submanifolds in manifolds with nonnegative sectional curvature. Both inequalities depend on the asymptotic volume ratio of the ambient manifold. © 2022 Wiley Periodicals LLC.

Topics & Concepts

MathematicsCurvatureRicci curvatureSectional curvatureManifold (fluid mechanics)Sobolev spaceInequalityScalar curvaturePure mathematicsSobolev inequalityRicci-flat manifoldMathematical analysisGeometryEngineeringMechanical engineeringGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsNumerical methods in inverse problems