Abstract
We show that in every class of conformally equivalent Riemannian spaces there exists at least one space whose exponential map is volume preserving near a given point. The proof is based on the solution of degenerated non-linear elliptic equations within the framework of weighted Hölder spaces.
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Günther, M. Conformal normal coordinates. Ann Glob Anal Geom 11, 173–184 (1993). https://doi.org/10.1007/BF00773455
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DOI: https://doi.org/10.1007/BF00773455