银河
发表于 2025-3-21 18:43:49
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魔鬼在游行
发表于 2025-3-21 20:29:10
Analysis on Manifolds and the Ricci Curvature, the properties of the Laplacian on a bounded Euclidean domain and on a compact Riemannian manifold are very similar, and so are the techniques of proofs. We can say that the difficulties of the latter case, compared with the former, are essentially conceptual.
为敌
发表于 2025-3-22 03:14:03
Textbook 19902nd editionry. Also, we present a -soft-proof of the Paul Levy-Gromov isoperimetric inequal ity, kindly communicated by G. Besson. Several people helped us to find bugs in the. first edition. They are not responsible for the persisting ones! Among them, we particularly thank Pierre Arnoux and Stefano Marchiaf
掺假
发表于 2025-3-22 06:46:10
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词根词缀法
发表于 2025-3-22 10:03:18
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Gingivitis
发表于 2025-3-22 16:34:08
Analysis on Manifolds and the Ricci Curvature, the properties of the Laplacian on a bounded Euclidean domain and on a compact Riemannian manifold are very similar, and so are the techniques of proofs. We can say that the difficulties of the latter case, compared with the former, are essentially conceptual.
HEDGE
发表于 2025-3-22 19:55:53
Springer-Verlag Berlin Heidelberg 1990
GROUP
发表于 2025-3-23 00:37:15
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蛛丝
发表于 2025-3-23 04:01:10
Riemannian Metrics,The Pythagorus theorem just says that the squared length of an infinitesimal vector, say in .., whose components are . and ., is .. + .. + ... Thus, the length of a parameterized curve .(.) = (.(.), .(.), .(.)) is given by the integral ..
FLEET
发表于 2025-3-23 06:01:09
Curvature,A parallel vector field in .. is just a constant field. Now, on a surface, there are generally no (even local) parallel vector fields. How much the parallel transport of a field along a small closed curve differ from the identity is measured in terms of the curvature of the surface, a function .: . → ..