释放
发表于 2025-3-25 04:28:11
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Bucket
发表于 2025-3-25 08:37:30
https://doi.org/10.1007/978-1-349-20201-0rs before discovering this result. It is the kind of theorem which could have waited dozens of years more before being discovered by another mathematician since, unlike so much of intellectual history, it was absolutely not in the air.
A保存的
发表于 2025-3-25 12:12:55
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Derogate
发表于 2025-3-25 18:58:19
https://doi.org/10.1007/978-1-349-16615-2ibrary around 1960. I should say not only that I liked it, but also that I found it very motivating and frequently advertised it. Moreover, the question is the first problem in the problem list Yau . It is only recently that I discovered that the question of best metric was posed much earlier by Hopf in Hopf 1932 , page 220.
异端邪说下
发表于 2025-3-25 20:48:52
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萤火虫
发表于 2025-3-26 01:27:14
B. D. Vujanovic,T. M. Atanackovicnly certain sorts of noncompact Riemannian manifolds to have a hope of obtaining results. Let us mention in particular the possibilities of examining manifolds with finite volume, those with prescribed asymptotic behaviour at infinity, for example quadratic decay,. quadratic curvature decay, volume behaviour, Euclidean asymptoticity, etc.
BUST
发表于 2025-3-26 04:33:39
Jonathan M. Borwein,Matthew P. SkerrittEuclidean geomeltry and the geometry of surfaces in E. that we looked at in the preceeding chapter turn out to be quite unsatisfactory for many reasons. We will review some of them here; they are not all logically related.
草本植物
发表于 2025-3-26 12:23:06
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失望未来
发表于 2025-3-26 13:22:17
B. D. Vujanovic,T. M. AtanackovicIn this chapter, up to and including §13.4, manifolds need not be compact, or even complete, but must have no boundary. Starting in §13.5, manifolds are once again assumed compact without boundary, unless otherwise stated.
crescendo
发表于 2025-3-26 19:40:56
B. D. Vujanovic,T. M. AtanackovicWe cannot give comprehensive references for this chapter, especially for the generalities. They appear in every book on differential geometry and Riemannian geometry. Only in some special instances will we give references.