Remarks on non-compact gradient Ricci solitons

By S. Pigola, Michele Rimoldi, A. G. Setti. 2009

212 citations recorded by the source corpus.

In this paper we show how techniques coming from stochastic analysis, such as stochastic completeness (in the form of the weak maximum principle at infinity), parabolicity and Lp-Liouville type results for the weighted Laplacian associated to the potential may be used to obtain triviality, rigidity results, and scalar curvature estimates for gradient Ricci solitons under Lp conditions on the relevant quantities.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2a4a8f2e6890f393479461d31b2706f7cb33a2dc

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Ricci almost solitons (2010, background): “The next result extends Theorem 3 in [27] to the case of almost solitons; see also [35].”
On Bach-flat gradient shrinking Ricci solitons (2011, result): “For an alternative proof of Lemma 2.2, see, e.g., the more recent work of Pigola-Rimoldi-Setti [25].”
Perelman’s entropy formula for the Witten Laplacian on Riemannian manifolds via Bakry–Emery Ricci curvature (2012, background): “Euclidean space. See Theorem 1 in [ 35 ] or Proposition 2 in [34].”
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).”
Analysis of weighted Laplacian and applications to Ricci solitons (2011, background): “Prior to our result, it was known from [24] that if |∇f | is bounded on M, then M is Einstein.”
On type-I singularities in Ricci flow (2010, background): “1 (Pigola-Rimoldi-Setti [18], Theorem 3).”