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Ebook: Elliptic PDEs on Compact Ricci Limit Spaces and Applications

Author: Shouhei Honda

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02.03.2024
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In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schr�dinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
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