scholarly journals Shi-type estimates of the Ricci flow based on Ricci curvature

2020 ◽  
Vol 20 (4) ◽  
pp. 1553-1580
Author(s):  
Chih-Wei Chen
Keyword(s):  
Ricci Curvature ◽  
Ricci Flow

scholarly journals Lower bounds on Ricci flow invariant curvatures and geometric applications

2015 ◽  
Vol 2015 (703) ◽  
Author(s):  
Thomas Richard
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Ricci Flow ◽  
Nonnegative Curvature ◽  
Curvature Operator ◽  
Nonnegative Ricci Curvature ◽  
Invariant Cones

AbstractWe consider Ricci flow invariant cones 𝒞 in the space of curvature operators lying between the cones “nonnegative Ricci curvature” and “nonnegative curvature operator”. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies

scholarly journals RICCI LOWER BOUND FOR KÄHLER–RICCI FLOW

2014 ◽  
Vol 16 (02) ◽  
pp. 1350053 ◽  
Author(s):  
ZHOU ZHANG
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
Ricci Flow ◽  
Finite Time ◽  
Ricci Flows ◽  
Time Singularities

We provide general discussion on the lower bound of Ricci curvature along Kähler–Ricci flows over closed manifolds. The main result is the non-existence of Ricci lower bound for flows with finite time singularities and non-collapsed global volume. As an application, we give examples showing that positivity of Ricci curvature would not be preserved by Ricci flow in general.

A note on Ricci flow with Ricci curvature bounded below

2017 ◽  
Vol 2017 (726) ◽  
Author(s):  
Xiuxiong Chen ◽  
Fang Yuan
Keyword(s):  
Ricci Curvature ◽  
Ricci Flow ◽  
Ricci Flows ◽  
Bounded Below

AbstractIn this note, we will prove that given a sequence of Ricci flows

scholarly journals Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds

2018 ◽  
Vol 2020 (5) ◽  
pp. 1481-1510 ◽  
Author(s):  
Fabio Cavalletti ◽  
Andrea Mondino
Keyword(s):  
Riemannian Manifold ◽  
Isoperimetric Inequality ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Ricci Flow ◽  
General Framework ◽  
Isoperimetric Inequalities ◽  
Optimal Transportation ◽  
Maximal Volume ◽  
Bounded Below

Abstract Motivated by Perelman’s Pseudo-Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it holds an almost euclidean isoperimetric inequality. The result is actually established in the more general framework of non-smooth spaces satisfying local Ricci curvature lower bounds in a synthetic sense via optimal transportation.

scholarly journals POSITIVITY OF RICCI CURVATURE UNDER THE KÄHLER–RICCI FLOW

2006 ◽  
Vol 08 (01) ◽  
pp. 123-133 ◽  
Author(s):  
DAN KNOPF
Keyword(s):  
Ricci Curvature ◽  
Ricci Flow ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bounded Curvature ◽  
Complex Dimension

In each complex dimension n ≥ 2, we construct complete Kähler manifolds of bounded curvature and non-negative Ricci curvature whose Kähler–Ricci evolutions immediately acquire Ricci curvature of mixed sign.

scholarly journals Bergman kernel along the Kähler–Ricci flow and Tian’s conjecture

2016 ◽  
Vol 2016 (717) ◽  
Author(s):  
Wenshuai Jiang
Keyword(s):  
Recent Work ◽  
Ricci Curvature ◽  
Ricci Flow ◽  
Bergman Kernel ◽  
Fano Manifolds ◽  
Bergman Kernels ◽  
Complex Dimension ◽  
Short Time

AbstractIn this paper, we study the behavior of Bergman kernels along the Kähler–Ricci flow on Fano manifolds. We show that the Bergman kernels are equivalent along the Kähler–Ricci flow for short time under certain condition on the Ricci curvature of the initial metric. Then, using a recent work of Tian and Zhang, we can solve a conjecture of Tian for Fano manifolds of complex dimension at most 3.

Holomorphic Functions on a Class of Kähler Manifolds With Nonnegative Curvature, I

2020 ◽  
Author(s):  
Bo Yang
Keyword(s):  
Asymptotic Behavior ◽  
Ricci Curvature ◽  
Ricci Flow ◽  
Polynomial Growth ◽  
Holomorphic Functions ◽  
Nonnegative Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Nonnegative Ricci Curvature

Abstract In this paper, we consider holomorphic functions of polynomial growth on complete Kähler manifolds with nonnegative curvature. We explain how their growth orders are related to the asymptotic behavior of Kähler–Ricci flow. The main result is to determine minimal orders of holomorphic functions on gradient Kähler–Ricci expanding solitons with nonnegative Ricci curvature.

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