Rotationally symmetric shrinking and ex - panding gradient Kahler - Ricci solitons

By Mikhail Feldman, T. Ilmanen, Dan Knopf. 2003

339 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c8dcb6be7d4dee0bfee7937b11d5fdcc03a19499

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Recent Progress on Ricci Solitons (2009, background): “(Noncompact gradient Kähler shrinkers) Feldman-IlmanenKnopf [47] found the first complete noncompact U(n)-invariant shrinking gradient Kähler-Ricci solitons, which are cone-like at infinity.”
On the evolution of a Hermitian metric by its Chern-Ricci form (2011, background): “It gives a flow of Kähler metrics whose behavior is deeply intertwined with the complex and algebro-geometric properties of M (see [8, 9, 15, 31, 32, 34, 35, 36, 37, 38, 40, 41, 45, 50, 51, 52, 56], for example).”
Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons (2011, background): “Mikhail Feldman, Tom Ilmanen, and Dan Knopf [7] constructed complete noncompact Kähler–Ricci shrinkers on the total spaces of k -th powers of tautological line bundles over the complex projective space CP n − 1 for 0 k n .”
Sharp logarithmic Sobolev inequalities on gradient solitons and applications (2008, background): “Nontrivial noncompact examples can be found in, for example, [18].”
An example of neckpinching for Ricci flow on $S^{n+1}$ (2004, background): “Another family of examples was constructed in [4].”
Comparison geometry for the Bakry-Emery Ricci tensor (2007, background): “These examples also have positive Ricci curvature but in the noncompact case there are Kahler Ricci shrinking solitons that do not have nonnegative Ricci curvature [11].”
RIGIDITY OF GRADIENT RICCI SOLITONS (2007, neutral): “For other examples of noncompact gradient solitons with large symmetry groups see [3, 4, 10, 13].”
On second variation of Perelman’s Ricci shrinker entropy (2010, methodology): “so [13] and the ﬁrst author [1] independently constructed a gradient Kahler-Ricci shrinking soliton on CP2#(−CP2), and Wang-Zhu [16] on CP2#(−2CP2), while in the noncompact case Feldman-Ilmanen-Knopf [8] constructed the U(2)-invariant gradient shrinking Kahler-Ricci solitons on the tautological line”
A Compactness Theorem for Complete Ricci Shrinkers (2010, neutral): “We manage to remove all volume and diameter assumptions, and we do not need any positivity assumptions for the curvatures nor pointwise curvature bounds (as the blow-down shrinker shows [18], even the Ricci curvature can have both signs).”
On Gradient Ricci Solitons (2009, background): “In higher dimensions, Koiso, Cao, Feldman, Ilmanen and Knopf constructed examples of gradient shrinking Ricci solitons that are not Einstein, [5, 13].”
Recent developments on the Hamilton’s Ricci Flow (2007, background): “Later, Feldman-Ilmanen-Knopf [33] also found such necklike Type I singularities on some noncompact Kähler manifold, the total space of certain holomorphic line bundle L−k over the complex projective space CPn.”
Geometry of Complete Gradient Shrinking Ricci Solitons (2009, background): “The noncompact Kähler shrinker of Feldman-Ilmanen-Knopf [19] in Example 1.”
On the Kähler-Ricci Flow on Projective Manifolds of General Type (2006, positive): “7This result below gives an affirmative answer to one of the problems listed in [6].”