Volume of small balls and sub-Riemannian curvature in 3D contact manifolds
Davide Barilari, Ivan Beschastnyi, Antonio Lerario
Abstract
We compute the asymptotic expansion of the volume of small subẊRiemannian balls in a contact 3-dimensional manifold, and we express the first meaningful geometric coefficients in terms of geometric invariants of the sub-Riemannian structure.
Topics & Concepts
MathematicsCurvature of Riemannian manifoldsRiemannian manifoldCurvatureRiemannian geometryVolume (thermodynamics)Manifold (fluid mechanics)Sectional curvatureContact geometryMinimal volumeMathematical analysisGeometryScalar curvaturePure mathematicsPhysicsEngineeringMechanical engineeringQuantum mechanicsGeometric Analysis and Curvature FlowsPoint processes and geometric inequalitiesGeometric and Algebraic Topology