Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds

Abstract

We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the $L^2$ Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.

typos corrected, to appear in Advances in Mathematics

References in corpus (3)

• $L^2$ Curvature Bounds on Manifolds with Bounded Ricci Curvature
• Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
• Compactness properties of Ricci flows with bounded scalar curvature

Cited by in corpus (4)

• New Volume Comparison results and Applications to degeneration of Riemannian metrics
• Bounds on harmonic radius and limits of manifolds with bounded Bakry-Émery Ricci curvature
• Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds
• Neumann Isoperimetric Constant Estimate for Convex Domains