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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The existence of generalized isothermal coordinates for higher-dimensional Riemannian manifolds
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by Jian Guo Cao PDF
Trans. Amer. Math. Soc. 324 (1991), 901-920 Request permission

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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 901-920
  • MSC: Primary 53B20; Secondary 53A30
  • DOI: https://doi.org/10.1090/S0002-9947-1991-0991959-1
  • MathSciNet review: 991959