搜索结果: 1-15 共查到“数学 Ricci flow”相关记录33条 . 查询时间(0.078 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Geometry of the Ricci flow singularity models
利玛窦流 奇点模型 几何形状
2023/4/25
The Ricci flow is a powerful tool in geometry to construct the canonical metric on a given manifold. It can be viewed as a nonlinear heat flow of the Riemannian metric and may develop finite time sing...
CURVATURE PINCHING ESTIMATE AND SINGULARITIES OF THE RICCI FLOW
SINGULARITIES CURVATURE PINCHING ESTIMAT
2015/8/17
In this paper, we first derive a pinching estimate on the traceless Ricci
curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then
we apply this estimate to study...
THE CONJUGATE HEAT EQUATION AND ANCIENT SOLUTIONS OF THE RICCI FLOW
ANCIENT SOLUTIONS CONJUGATE HEAT EQUATION
2015/8/17
We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation evolving under the Ricci flow. As a consequence, for dimension 4 and
higher, we show that the backward ...
BACKWARD RICCI FLOW ON LOCALLY HOMOGENEOUS THREE-MANIFOLDS
THREE-MANIFOLDS LOCALLY HOMOGENEOUS
2015/8/17
In this paper, we study the backward Ricci flow on locally homogeneous
3-manifolds. We describe the long time behavior and show that, typically and after
a proper re-scaling, there is converge...
DIFFERENTIAL HARNACK ESTIMATES FOR BACKWARD HEAT EQUATIONS WITH POTENTIALS UNDER THE RICCI FLOW
HARNACK ESTIMATES WITH POTENTIALS UNDER THE RICCI FLOW
2015/8/17
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities
for positive solutions of backward hea...
FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE RICCI FLOW
GEOMETRIC OPERATORS UNDER FLOW
2015/8/17
In this paper, we prove that the first eigenvalues of
−∆ + cR (c ≥
1
4
) is nondecreasing under the Ricci flow. We also
prove the monotonicity under the normalized Ricci &...
《Ricci Flow and the Sphere Theorem》。
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...
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...
Evolution of curvature along the hyperbolic Ricci flow
Evolution of curvature hyperbolic Ricci
2018/4/19
We consider the hyperbolic geometric flow $\frac{\partial^2 g(t)}{\partial t ^2} = −2Ric_g(t)$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Usi...
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2018/4/19
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 the relat...
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...
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...