Liu, Gang ( 刘 钢 )
| Title： | Professor |
|---|---|
| Department： | Pure Mathematics |
| Office： | Room 216, Math Building |
| Telephone： | 54342646-216 |
| Email： | gliu@math.ecnu.edu.cn |
| Homepage： | http://math.ecnu.edu.cn/~gliu |
| Homepage2： | https://faculty.ecnu.edu.cn/_s42/lg2/main.psp |
Research Interest
Geometric Analysis, Complex Geometry
Resume
Resume:
Selected Publications
Papers:
(with S. J. Wu) Convex hull theorem for multiple connected domains
in the plane with an estimate of the quasiconformal constant,
Sci. China. Ser A 52(2009), no 5, 932-940.
Local volume comparison for Kahler manifolds, Pacific J. Math.
254 (2011), no. 2, 345-360.
A short proof to the rigidity of volume entropy, Math. Res. Lett.
18(2011), no. 1, 151-153.
Kahler manifolds with Ricci curvature lower bound, Asian J. Math.
18(2014), 69-100.
3-manifolds with nonnegative Ricci curvature, Invent. Math (2013).
193, 367-375.
Compact Kahler manifolds with nonpositive bisectional curvature,
Geom. Func. Anal. 24(2014), 1591-1607.
Stable weighted minimal surfaces in manifolds with nonnegative
Bakry-Emery tensor, Comm. Anal. Geom. 21(2013), 1061-1079 .
Three circle theorem and dimension estimate for holomorphic functions
on Kahler manifolds, Duke. Math. J. 15 (2016), 2899-2919.
On the volume growth of Kahler manifolds with nonnegative bisectional
curvature, J. Di . Geom. 102(2016), no 3, 485-500.
On the tangent cone of Kahler manifolds with Ricci curvature
lower bound, Math. Ann. 370 (2018), 649-667.
Gromov-Hausdor limits of Kahler manifolds and the nite generation
conjecture, Ann. of Math. (2) 184 (2016), no. 3, 775-815.
Gromov-Hausdor limits of Kahler manifolds with bisectional curvature
lower bound I, Comm. Pure. Appl. Math. 71(2018), 267-
303.
On Yau's uniformization conjecture, Camb. J. Math. 7(2019),
no. 1-2, 33-70.
(with Yuan Yuan) Diameter rigidity for Kahler manifolds with
positive bisectional curvature, Math. Z. 290(2018), 1055-1061.
Compactification of certain noncompact Kahler manifolds with
nonnegative Ricci curvature, arxiv: 1706.06067.
(with Gabor Szekelyhidi) Gromov-Hausdorff limits of Kahler manifolds
with Ricci curvature bounded below, arxiv: 1804.08567.
(with Gabor Szekelyhidi) Gromov-Hausdor limits of Kahler manifolds
with Ricci curvature bounded below II, Accepted by Comm.
Pure. Appl. Math.
Dimension estimate of polynomial growth holomorphic functions,
preprint.
Recent Publications(From MathSciNet)
MR4680331
Reviewed
Liu, Gang Kähler manifolds with curvature bounded below.
ICM—International Congress of Mathematicians. Vol. 4. Sections 5–8,
2576–2592, EMS Press, Berlin, [2023], ©2023. (Reviewer: Yanir A. Rubinstein) 53C55 (32Q15)
Publication Year 2023
Indexed 2024-04-06
Review Published2025-11-13
MR4543771
Reviewed
Liu, Gang A brief survey on dimension estimate of holomorphic functions on Kähler manifolds.
J. Geom. Anal. 33 (2023), no. 4, Paper No. 118, 12 pp. 53C55 (32Q10 32Q15)
Publication Year 2023
Indexed 2023-03-27
Review Published2023-05-03
MR4408432
Reviewed
Liu, Gang; Székelyhidi, Gábor Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below.
Geom. Funct. Anal. 32 (2022), no. 2, 236–279. (Reviewer: Francesco Pediconi) 53C55 (53C21)
Publication Year 2022
Indexed 2022-05-23
Review Published2022-10-20
MR4319925
Reviewed
Liu, Gang Dimension estimate of polynomial growth holomorphic functions.
Peking Math. J. 4 (2021), no. 2, 187–202. (Reviewer: Haozhao Li) 53C55 (32Q15 53C21)
Publication Year 2021
Indexed 2021-12-04
Review Published2023-05-08
MR4230063
Reviewed
Liu, Gang; Székelyhidi, Gábor Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below II.
Comm. Pure Appl. Math. 74 (2021), no. 5, 909–931. (Reviewer: Joeri Van der Veken) 53C55 (53C21)
Publication Year 2021
Indexed 2021-05-18
Review Published2023-05-23
MR4224050
Reviewed
Liu, Gang Compactification of certain Kähler manifolds with nonnegative Ricci curvature.
Adv. Math. 382 (2021), Paper No. 107652, 27 pp. (Reviewer: Leonardo Biliotti) 53C55 (32Q05 32Q15 53C21)
Publication Year 2021
Indexed 2021-04-30
Review Published2022-01-29
MR3971904
Reviewed
Liu, Gang A survey on recent progress of Yau's uniformization conjecture.
Proceedings of the Seventh International Congress of Chinese Mathematicians. Vol. II,
285–299, Adv. Lect. Math. (ALM), 44, Int. Press, Somerville, MA, 2019. 53C55 (32G15 32Q30)
Publication Year 2019
Indexed 2020-03-13
Review Published2020-03-25
MR3922359
Reviewed
Liu, Gang On Yau's uniformization conjecture.
Camb. J. Math. 7 (2019), no. 1-2, 33–70. (Reviewer: Shan Tai Chan) 32Q15 (32M25 32Q30)
Publication Year 2019
Indexed 2019-05-20
Review Published2020-05-21
MR3856844
Reviewed
Liu, Gang; Yuan, Yuan Diameter rigidity for Kähler manifolds with positive bisectional curvature.
Math. Z. 290 (2018), no. 3-4, 1055–1061. (Reviewer: Caner Koca) 53C55 (32Q15 53C24)
Publication Year 2018
Indexed 2018-11-14
Review Published2019-06-02
MR3747498
Reviewed
Liu, Gang On the tangent cone of Kähler manifolds with Ricci curvature lower bound.
Math. Ann. 370 (2018), no. 1-2, 649–667. (Reviewer: Matthew B. Stenzel) 53C55 (32Q15 53C23)
Publication Year 2018
Indexed 2018-03-15
Review Published2018-09-14
MR3745153
Reviewed
Liu, Gang Gromov-Hausdorff limits of Kähler manifolds with bisectional curvature lower bound.
Comm. Pure Appl. Math. 71 (2018), no. 2, 267–303. (Reviewer: Tao Zheng) 53C55 (53C21)
Publication Year 2018
Indexed 2018-03-13
Review Published2019-03-21
MR3557275
Reviewed
Liu, Gang Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds.
Duke Math. J. 165 (2016), no. 15, 2899–2919. (Reviewer: J. T. Davidov) 53C21 (32A10 32Q30 53C55)
Publication Year 2016
Indexed 2016-12-23
Review Published2017-05-22
MR3466805
Reviewed
Liu, Gang On the volume growth of Kähler manifolds with nonnegative bisectional curvature.
J. Differential Geom. 102 (2016), no. 3, 485–500. (Reviewer: Juan de D. Pérez) 53C55 (32Q15 53C20)
Publication Year 2016
Indexed 2016-05-26
Review Published2016-11-09
MR3261635
Reviewed
Liu, Gang Compact Kähler manifolds with nonpositive bisectional curvature.
Geom. Funct. Anal. 24 (2014), no. 5, 1591–1607. (Reviewer: Antonella Nannicini) 53C55 (53C21)
Publication Year 2014
Indexed 2014-11-10
Review Published2015-02-17
MR3215340
Reviewed
Liu, Gang Kähler manifolds with Ricci curvature lower bound.
Asian J. Math. 18 (2014), no. 1, 69–99. (Reviewer: Cornelia-Livia Bejan) 53C55 (53C20)
Publication Year 2014
Indexed 2014-07-30
Review Published2014-11-20
MR3167307
Thesis
Liu, Gang On manifolds with Ricci curvature lower bound and Kahler manifolds with nonpositive bisectional curvature.
Thesis (Ph.D.)–University of Minnesota.
2013. 112 pp. ISBN: 978-1303-19256-2, ProQuest LLC
Publication Year 2013
Indexed 2014-02-21
MR3152972
Reviewed
Liu, Gang Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor.
Comm. Anal. Geom. 21 (2013), no. 5, 1061–1079. (Reviewer: João Lucas Marques Barbosa) 53A10 (58E12)
Publication Year 2013
Indexed 2014-03-27
Review Published2014-06-12
MR3090181
Reviewed
Liu, Gang 3-manifolds with nonnegative Ricci curvature.
Invent. Math. 193 (2013), no. 2, 367–375. (Reviewer: David J. Wraith) 53C20 (53A10 53C21)
Publication Year 2013
Indexed 2013-11-14
Review Published2014-04-02
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