Results 11 to 20 of about 420 (130)
Volume Growth Estimates of Gradient Ricci Solitons
The Journal of Geometric Analysis, 2022 AbstractIn this paper, we survey the volume growth estimates for shrinking, steady, and expanding gradient Ricci solitons. Together with the known results, we also prove some new volume growth estimates for expanding gradient Ricci solitons.
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
openaire +4 more sources
On the Potential Function of Gradient Steady Ricci Solitons [PDF]
Journal of Geometric Analysis, 2011 A steady gradient Ricci soliton is a Riemannian manifold \((M,g)\) together with a real potential function \(f\) satisfying \(\text{Ric}+ \text{Hess\,}f= 0\). For a complete and noncompact \(M\), it is shown that the infimum of the potential function decays linearly. In particular it cannot be bounded unless it is constant.
openaire +3 more sources
Gradient ricci solitons on multiply warped product manifolds [PDF]
, 2018 We consider gradient Ricci solitons on multiply warped product manifolds. We find the necessary and sufficient conditions for multiply warped product manifolds to be gradient Ricci ...
Ozgur, Cihan +2 more
core +4 more sources
On Type-I singularities in Ricci flow [PDF]
, 2011 07.02.13 KB. Accepted version ok to add to Spiral. IP/Sherpa.We define several notions of singular set for Type I Ricci flows and show that they all coincide.
Topping, Peter +5 more
core +1 more source
Stability of gradient Kähler-Ricci solitons [PDF]
Communications in Analysis and Geometry, 2005 We study stability of non-compact gradient Kaehler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kaehler potential of the soliton will converge to the original soliton under Kaehler-Ricci flow as time tends to infinity. To
Chau, Albert, Schnuerer, Oliver C.
openaire +2 more sources
The Weyl tensor of gradient Ricci solitons [PDF]
Geometry & Topology, 2016 This paper derives new identities for the Weyl tensor on a gradient Ricci soliton, particularly in dimension four. First, we prove a Bochner-Weitzenböck type formula for the norm of the self-dual Weyl tensor and discuss its applications, including connections between geometry and topology.
Cao, Xiaodong, Tran, Hung
openaire +3 more sources
On the completeness of gradient Ricci solitons [PDF]
Proceedings of the American Mathematical Society, 2009 A gradient Ricci soliton is a triple ( M , g , f
openaire +2 more sources
Isometry theorem of gradient Shrinking Ricci solitons [PDF]
Journal of Geometry and Physics, 2021 In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also the reciprocal of the potential function is subharmonic, then the manifold is isometric to the Euclidean sphere.
Shaikh, Absos Ali, Mondal, Chandan Kumar
openaire +3 more sources
Gradient Kähler–Ricci solitons and periodic orbits [PDF]
Communications in Analysis and Geometry, 2000 We study Hamiltonian dynamics of gradient Kaehler-Ricci solitons that arise as limits of dilations of singularities of the Ricci flow on compact Kaehler manifolds. Our main result is that the underlying spaces of such gradient solitons must be Stein manifolds.
Cao, Huai-Dong, Hamilton, Richard S.
openaire +3 more sources
On the classification of gradient Ricci solitons [PDF]
Geometry & Topology, 2010 14 pages. case.
Petersen, Peter, Wylie, William
openaire +3 more sources