Kähler manifolds with Ricci curvature lower bound

Gang Liu

doi:10.4310/AJM.2014.v18.n1.a4

Kähler manifolds with Ricci curvature lower bound

Gang Liu^*

^*Corresponding author for this work

University of California at Berkeley

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

On Kähler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov's relative volume comparison, Bonnet-Meyers theorem, and Yau's gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the Kähler structure.

Original language	English
Pages (from-to)	69-100
Number of pages	32
Journal	Asian Journal of Mathematics
Volume	18
Issue number	1
DOIs	https://doi.org/10.4310/AJM.2014.v18.n1.a4
State	Published - 2014
Externally published	Yes

Keywords

Comparison theorem
Kähler manifold

Access to Document

10.4310/AJM.2014.v18.n1.a4

Cite this

@article{af52ffe4f7f94710a61730e581cfd861,

title = "K{\"a}hler manifolds with Ricci curvature lower bound",

abstract = "On K{\"a}hler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov's relative volume comparison, Bonnet-Meyers theorem, and Yau's gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the K{\"a}hler structure.",

keywords = "Comparison theorem, K{\"a}hler manifold",

author = "Gang Liu",

note = "Publisher Copyright: {\textcopyright} 2014 International Press.",

year = "2014",

doi = "10.4310/AJM.2014.v18.n1.a4",

language = "英语",

volume = "18",

pages = "69--100",

journal = "Asian Journal of Mathematics",

issn = "1093-6106",

publisher = "International Press, Inc.",

number = "1",

}

TY - JOUR

T1 - Kähler manifolds with Ricci curvature lower bound

AU - Liu, Gang

PY - 2014

Y1 - 2014

N2 - On Kähler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov's relative volume comparison, Bonnet-Meyers theorem, and Yau's gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the Kähler structure.

AB - On Kähler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov's relative volume comparison, Bonnet-Meyers theorem, and Yau's gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the Kähler structure.

KW - Comparison theorem

KW - Kähler manifold

UR - https://www.scopus.com/pages/publications/84921441515

U2 - 10.4310/AJM.2014.v18.n1.a4

DO - 10.4310/AJM.2014.v18.n1.a4

M3 - 文章

AN - SCOPUS:84921441515

SN - 1093-6106

VL - 18

SP - 69

EP - 100

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 1

ER -

Kähler manifolds with Ricci curvature lower bound

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this