In his paper [2], Paul Ehrlich write

> In [1], Aubin stated a theorem which implied as a corollary that **_if a manifold
$M$ admits a Riemannian metric with nonnegative Ricci curvature and
all Ricci curvatures positive at some point, then $M$ admits a metric of everywhere
positive Ricci curvature._** It appears the proof in [1] is incomplete
and the uniformity and correctness of Aubin's estimates even in the compact
case are not clear.

Aubin paper is a bit technical so I want to know did Paul Ehrlich have a valid point, and if so, what is it, specifically?

What specifically is the gap in Aubin's argument about positive Ricci curvature that Paul Ehrlich alludes to?

**Note 1:** As far as I understand main part of the proof of wanted theorem is in pp. 397-399.

**Note 2:** Most of people that cited Aubin's paper (about positive Ricci curvature), also cited Paul Ehrlich's paper as well. Note also that most of papers that referred to Aubin's paper is because of results about scalar curvature and Yamabe problem.

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  [1]: <cite authors="Aubin, T.">_Aubin, T._, [**Métriques riemanniennes et courbure**](http://dx.doi.org/10.4310/jdg/1214429638), J. Differ. Geom. 4, 383-424 (1970). [ZBL0212.54102](https://zbmath.org/?q=an:0212.54102).</cite>

  [2]: <cite authors="Ehrlich, Paul">_Ehrlich, Paul_, [**Metric deformations of curvature. I: Local convex deformations**](http://dx.doi.org/10.1007/BF00145952), Geom. Dedicata 5, 1-23 (1976). [ZBL0345.53024](https://zbmath.org/?q=an:0345.53024).</cite>