Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1991-0991959-1
MathSciNet review: 991959
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $p$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53B20, 53A30

Retrieve articles in all journals with MSC: 53B20, 53A30


Additional Information

Article copyright: © Copyright 1991 American Mathematical Society