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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The existence of generalized isothermal coordinates for higher-dimensional Riemannian manifolds


Author: Jian Guo Cao
Journal: Trans. Amer. Math. Soc. 324 (1991), 901-920
MSC: Primary 53B20; Secondary 53A30
MathSciNet review: 991959
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Abstract: We shall show that, for any given point $ p$ on a Riemannian manifold $ (M,{g^0})$, there is a pointwise conformal metric $ g = \Phi {g^0}$ in which the $ g$-geodesic sphere centered at $ p$ with radius $ r$ has constant mean curvature $ 1/r$ for all sufficiently small $ r$. Furthermore, the exponential map of $ g$ at $ p$ is a measure preserving map in a small ball around $ p$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-0991959-1
PII: S 0002-9947(1991)0991959-1
Article copyright: © Copyright 1991 American Mathematical Society