1975/01/01 by Shing–Tung Yau · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #advanced mathematical theories #Quantum chaos and dynamical systems #Isoperimetric inequality #Riemannian manifold #Mathematics #Mathematical analysis #Manifold (fluid mechanics) #Eigenvalues and eigenvectors #Pure mathematics #Riemannian geometry #Constant (computer programming) #Physics #Computer science
paper · pdf · doi:10.24033/asens.1299
openalex publication_date 1975/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
Given a compact Riemannian manifold M^ the Poincare inequality tells us that for any smooth function/defined on M with / = 0, we can estimate f 2 in terms of | V/ P. JM JM JM By the minimax-principle, one knows that the best possible constant in the Poincare inequality is given by the first eigenvalue of the Laplacian. While this constant has analytic importance, it also gives strong insight in the geometry of the manifold.