Analysis on Riemannian manifolds and Ricci curvature
Analysis on Riemannian manifolds stems from the following simple fact: the classical Laplace operator has an exact Riemannian analog. Indeed, the properties of the Laplacian on a bounded Euclidean domain and on a compact Riemannian manifold are very similar, and so are the proofs. It can be said that the difficulties of the latter case, compared with the former, are essentially conceptual.
KeywordsRiemannian Manifold Neumann Problem Ricci Curvature Isoperimetric Inequality Compact Riemannian Manifold
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