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On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth. (English) Zbl 0682.53045
The paper is concerned with the construction of certain Euclidean-like coordinate systems at infinity of complete Riemannian manifolds with curvature decay (for the Riemann and Ricci curvature tensors) and volume ascent of balls of prescribed order $$<-2$$ and n, respectively. In particular, a conjecture of H. Nakajima on Ricci-flat manifolds of dimension $$\geq 4$$ can be answered with these methods [J. Fac. Sci., Univ. Tokyo, Sect. I A 35, 411-424 (1988; Zbl 0655.53037)]. The proofs are highly technical, consisting of numerous estimates, and relying on results on Laplacian and Hessian comparison theorems, harmonic coordinates, Gromov’s convergence theorem and J. Moser’s iteration scheme.
Reviewer: R.Walter

##### MSC:
 53C20 Global Riemannian geometry, including pinching
Full Text:
##### References:
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