Geodesic
Ricci DeTurck flow on incomplete manifolds
Documenta mathematica, Tome 27 (2022), pp. 1169-1212.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper we construct a Ricci DeTurck flow on any incomplete Riemannian manifold with bounded curvature. The central property of the flow is that it stays uniformly equivalent to the initial incomplete Riemannian metric, and in that sense preserves any given initial singularity structure. Together with the corresponding result by \textit{W.-X. Shi} for complete manifolds [J. Differ. Geom. 30, No. 1, 223--301 (1989; Zbl 0676.53044)], this gives that any (complete or incomplete) manifold of bounded curvature can be evolved by the Ricci DeTurck flow for a short time.
Classification : 53E20, 53C20
Keywords: Ricci flow, incomplete manifolds, initial singularity structure 
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     author = {Marxen, Tobias and Vertman, Boris},
     title = {Ricci {DeTurck} flow on incomplete manifolds},
     journal = {Documenta mathematica},
     pages = {1169--1212},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a37/}
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Marxen, Tobias; Vertman, Boris. Ricci DeTurck flow on incomplete manifolds. Documenta mathematica, Tome 27 (2022), pp. 1169-1212. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a37/