Geodesic
Ricci DeTurck flow on incomplete manifolds
Documenta mathematica, Tome 27 (2022), pp. 1169-1212 Cet article a éte moissonné depuis la source EMS Press

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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 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.
DOI : 10.4171/dm/894
Classification : 53C20, 53E20
Mots-clés : Ricci flow, incomplete manifolds, initial singularity structure 
@article{10_4171_dm_894,
     author = {Tobias Marxen and Boris Vertman},
     title = {Ricci {DeTurck} flow on incomplete manifolds},
     journal = {Documenta mathematica},
     pages = {1169--1212},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/894},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/894/}
}
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Tobias Marxen; Boris Vertman. Ricci DeTurck flow on incomplete manifolds. Documenta mathematica, Tome 27 (2022), pp. 1169-1212. doi: 10.4171/dm/894

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