Noncompact shrinking four solitons with nonnegative curvature

By A. Naber. 2010

256 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1ddbd74a7e54a1c72f7fdb5a1f77d73cff609f24

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the geometry of gradient einstein-type manifolds (2014, unknown): “[25], [28], [39], [22], [38], [48], [37], [40], [10], [7], [14], [42], [11], [13], [8], [6], [33], [5] and references therein).”
Remarks on non-compact gradient Ricci solitons (2009, background): “with v ∈ R m such that |v| = 1. In fact, a kind of converse also holds; [ 9 ,11,20].”
On the classification of gradient Ricci solitons (2007, methodology): “Also see Naber’s paper [ 24 ] for a di¤erent argument in the 3-dimensional case.”
Geometry of shrinking Ricci solitons (2014, background): “ quotient of the sphere S 3,or R ,or S2 ×R.His result played a crucial role in the aﬃrmative resolution of the Poincar´e conjecture. The extra conditions were later removed through the eﬀort of Naber [23], Ni and Wallach [24], and Cao, Chen and Zhu [3]. We should refer the readers to [1] for the cla”
Heat kernel on Ricci shrinkers (2019, methodology): “In dimension 3, we know that R, S 2 × R, S 3 and their quotients are all possible Ricci shrinkers, based on the work of Perelman [47], Petersen-Wylie [48], Naber [44], Ni-Wallach [46] and Cao-Chen-Zhu [8].”
On Locally Conformally Flat Gradient Shrinking Ricci Solitons (2008, background): “The classification of complete noncompact gradient Ricci solitons has been studied by many authors very recently under various conditions, for example, see [ Nab07 ], [NW07], [PW07] and [FMZ08].”
Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature (2021, unknown): “In the shrinking case, classification results for gradient Ricci solitons have been obtained by many authors under various curvature conditions on the Weyl tensor, e.g., [7; 9; 10; 17; 20; 21; 24; 28; 29; 30; 31; 33; 35; 36], etc.”
Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, background): “For example, Naber [44] has shown that a four-dimensional complete noncompact nonflat shrinker of bounded nonnegative curvature operator must be a finite quotient of the standard solitons on R×S3 or R2×S2.”
On type-I singularities in Ricci flow (2010, methodology): “This is based on a version of Perelman’s reduced length and volume based at the singular time, developed independently by the first author [7] and Naber [15].”
Rigidity of gradient Einstein shrinkers (2013, background): “In dimension four, under the assumption of bounded nonnegative curvature operator, the most significant classification result has been obtained by Naber [9], where the author proves that any noncompact Ricci shrinker of this type is isometric to R4 or to a finite quotient of either S2×R2 or S3×R.”
Immortal homogeneous Ricci flows (2017, background): “case of ﬁnite extinction time, assuming a Type-I behavior of the evolved curvature tensors, it could then be shown that any essential blow-up sequence subconverges to a nonﬂat, gradient Ricci soliton [Nab10], [EMT11]. By contrast, for immortal Ricci ﬂow solutions, assuming a Type-III behavior of the”