Regularity of Kähler–Ricci flows on Fano manifolds

G Tian, Z Zhang - 2016 - projecteuclid.org
In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-
manifolds with Ricci curvature bounded in L p-norm for some p> n. Using this regularity …

[PDF][PDF] Manifolds with a lower Ricci curvature bound

G Wei - arXiv preprint math/0612107, 2006 - arxiv.org
arXiv:math/0612107v1 [math.DG] 4 Dec 2006 Page 1 arXiv:math/0612107v1 [math.DG] 4 Dec
2006 Manifolds with A Lower Ricci Curvature Bound Guofang Wei ∗ Abstract This paper is a …

Comparison geometry for integral Bakry–Émery Ricci tensor bounds

JY Wu - The Journal of Geometric Analysis, 2019 - Springer
We prove mean curvature and volume comparison estimates on smooth metric measure
spaces when their integral Bakry–Émery Ricci tensor bounds, extending Wei–Wylie's …

Stability of metric measure spaces with integral Ricci curvature bounds

C Ketterer - Journal of Functional Analysis, 2021 - Elsevier
In this article we study stability and compactness wrt measured Gromov-Hausdorff
convergence of smooth metric measure spaces with integral Ricci curvature bounds. More …

Chiti-type reverse Hölder inequality and torsional rigidity under integral Ricci curvature condition

H Chen - Potential Analysis, 2022 - Springer
In this paper, we prove a reverse Hölder inequality for the eigenfunction of the Dirichlet
problem on domains of a compact Riemannian manifold with the integral Ricci curvature …

Integral Radial m-Bakry–Émery Ricci Curvatures, Riccati Inequalities, and Ambrose-type Theorems

H Tadano - Results in Mathematics, 2024 - Springer
Inspired by a recent work due to J.-Y. Wu (Potential Anal 58: 203–223, 2023), we prove
several new compactness criteria for complete Riemannian manifolds via integral radial m …

[PDF][PDF] Comparison geometry for Ricci curvature

X Dai, G Wei - preprint, 2012 - math.ucsb.edu
A Ricci curvature bound is weaker than a sectional curvature bound but stronger than a
scalar curvature bound. Ricci curvature is also special that it occurs in the Einstein equation …

Ricci curvature integrals, local functionals, and the Ricci flow

Y Ma, B Wang - Transactions of the American Mathematical Society …, 2023 - ams.org
Consider a Riemannian manifold $(M^{m}, g) $ whose volume is the same as the standard
sphere $(S^{m}, g_ {round}) $. If $ p\!>\!\frac {m}{2} $ and $\int _ {M}\!\left\{Rc\!-\!(m\!-\! 1) …

Myers' Type Theorem for Integral Bakry–Émery Ricci Tensor Bounds

F Li, JY Wu, Y Zheng - Results in Mathematics, 2021 - Springer
In this paper we first discuss weighted mean curvature and volume comparisons on smooth
metric measure space (M, g, e^-f dv)(M, g, e-fdv) under the integral Bakry–Émery Ricci …

Liouville Type Theorem about -harmonic 1 form, -harmonic map and harmonic form

X Cao - arXiv preprint arXiv:2210.14024, 2022 - arxiv.org
In this paper, we will use the normalized intetral Ricci curvature to investigate Liouville type
property of $ p $ harmonic function on Riemannian manifold. secondly, we will use the BiRic …