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Deformation of $$C^0$$ Riemannian metrics in the direction of their Ricci curvature. (English) Zbl 1034.58008
The author uses the dual Ricci-harmonic map flow in order to obtain some results about the non smooth Riemannian metric tensors on finite dimensional smooth manifolds. As an application, he studies the evolution of metrics which arise in the study of spaces whose curvature is bounded from above and below in the sense of Aleksandrov and whose curvature operator is non-negative. Such metrics may always be deformed to a smooth metric having the same properties in a strong sense.

##### MSC:
 58D17 Manifolds of metrics (especially Riemannian) 58D27 Moduli problems for differential geometric structures 58H15 Deformations of general structures on manifolds
##### Keywords:
Riemannian metrics; Ricci flow; Ricci-harmonic map flow
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