Gradient and Hessian Estimates for Dirichlet and Neumann Eigenfunctions
classification
🧮 math.DG
keywords
curvaturedirichleteigenfunctionsestimatesgradienthessianneumannsharp
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We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.
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