搜索结果: 1-15 共查到“微分几何学 THE RICCI”相关记录23条 . 查询时间(0.093 秒)
Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Local pinching estimates in 3-dim Ricci flow
Local pinching estimates 3-dim Ricci flow Differential Geometry
2012/6/30
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on a...
Ricci surfaces
minimal surfaces Ricci condition generalized Killing spinors Ricci surfaces
2012/6/29
A Ricci surface is a Riemannian 2-manifold $(M,g)$ whose Gaussian curvature $K$ satisfies $K\Delta K+g(dK,dK)+4K^3=0$. Every minimal surface isometrically embedded in $\mathbb{R}^3$ is a Ricci surface...
Remarks on the extension of the Ricci flow
Remarks the extension of the Ricci flow Differential Geometry
2012/6/19
We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.
New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow
New logarithmic Sobolev inequalities ε-regularity theorem Ricci flow Differential Geometry
2012/5/24
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
No breathers theorem for some noncompact Ricci flows
No breathers theorem noncompact Ricci flows Differential Geometry
2012/5/24
Under suitable conditions near infinity and assuming boundedness of curvature tensor, we prove a no breathers theorem in the spirit of Ivey-Perelman for some noncompact Ricci flows. These include Ricc...
A note on Canonical Ricci forms on 2-step nilmanifolds
note Canonical Ricci forms 2-step nilmanifolds
2012/2/29
In this note we prove that any left-invariant almost Hermitian structure on a 2-step nilmanifold is Ricci-flat with respect to the Chern connection and that it is Ricci -flat with respect to another c...
Abstract: We simplify and improve the curvature estimates in the paper: On the conditions to extend Ricci flow(II). Furthermore, we develop some volume estimates for the Ricci flow with bounded scalar...
Abstract: We develop some estimates under the Ricci flow and use these estimates to study the blowup rates of curvatures at singularities. As applications, we obtain some gap theorems:
$\displaystyl...
Bach-flat gradient steady Ricci solitons
Bach-flat gradient Ricci solitons Differential Geometry
2011/9/19
Abstract: In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci solitons with positive Ricci curvature is isometric to the Bryant soliton. We also show th...
Bounds on volume growth of geodesic balls under Ricci flow
geodesic balls under Ricci flow Differential Geometry Analysis of PDEs
2011/9/16
Abstract: We prove a so called $\kappa$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar cur...
Supremum of Perelman's entropy and Kahler-Ricci flow on a Fano manifold
Kahler-Ricci flow Kahler-Ricci solitons Perelman entropy
2011/9/15
Abstract: In this paper, we extend the method in [TZhu5] to study the energy level $L(\cdot)$ of Perelman's entropy $\lambda(\cdot)$ for K\"ahler-Ricci flow on a Fano manifold. Consequently, we first ...
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2011/9/13
Abstract: In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that...
Some geometric analysis on generic Ricci solitons
Ricci solitons X–Laplacian scalar curvature estimates maximum principles volume estimates
2011/9/6
Abstract: We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.
Abstract: The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetime...