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Zhu, Meng ( 朱 萌 ) 
Title: Professor
Department: Pure Mathematics
Office: Room 327, Math Building
Telephone: 54342646-327
Email: mzhu@math.ecnu.edu.cn
Homepage: http://math.ecnu.edu.cn/~mzhu
Homepage2: https://faculty.ecnu.edu.cn/_s42/zm2/main.psp
Research Interest
Differential Geometry and Geometric Analysis
Resume
Resume

教育经历 (Education):
2006.8-2012.5 美国里海大学(Lehigh University),博士(Ph.D. in Mathematics)
1999.9-2003.6 浙江大学(Zhejiang University),学士(B.S. in Mathematics)


工作经历(Working Experience):
2014.9至今, 华东师范大学(East China Normal University),紫江青年学者(Zijiang Young Research Professor)
2014.10-2017.6, 美国加州大学河滨分校(UC Riverside),访问助理教授(Visiting Assistant Proressor)
2012.9-2014.8, 复旦大学上海数学中心(Shanghai Center for Mathematical Sciences, Fudan University),博士后(Postdoc Fellow)

Selected Publications

Papers:
(1) Qi S. Zhang and Meng Zhu, Bounds on harmonic radius and limits of manifolds with bounded Bakry-Emery Ricci curvature, to appear in J. Geom. Anal.(2018), https://doi.org/10.1007/s12220-018-0072-9


(2) Qi S. Zhang and Meng Zhu, Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions, J. Func. Anal. 275 (2018), 478-515


(3) Huai-Dong Cao and Meng Zhu, Aronson-Benilan estimates for the fast diffusion equation under the Ricci flow, Nonliear Analysis 170 (2018), 258-281.


(4) Meng Zhu, On the relation between Ricci solitons and Ricci-Harmonic solitons, J. Math. Anal. Appl. 447 (2017), Issue 2, 882


(5) Qi S. Zhang and Meng Zhu, Li-Yau gradient bound for collapsing manifolds under integral curvature condition, Proc. Amer. Math. Soc. 145 (2017), 3117-3126


(6) Meng Zhu, Davies type estimate and the heat kernel bound under the Ricci flow, Trans. Amer. Math. Soc. 368 (2016), 1663-1680


(7) Huai-Dong Cao and Meng Zhu, Aronson-Benilan estimates for the porous medium equation under the Ricci flow, J. Math. Pure. Appl. 104 (2015), Issue 4, 729-748


(8) Qiang Chen and Meng Zhu, On rigidity of gradient Kahler-Ricci solitons with harmonic Bochner tensor, Proc. Amer. Math. Soc. 140 (2012), No. 11, 4017-4025.


(9) Huai-Dong Cao and Meng Zhu, On second variation of Perelman's Ricci shrinker entropy, Math. Ann. 353 (2012), No. 3, 747-763.


(10) Meng Zhu, The second variation of the Ricci expander entropy, Pacific J. Math. 251 (2011), No. 2, 499-510.


(11) Huai-Dong Cao and Meng Zhu, A note on compact Kahler-Ricci flow with positive bisectional curvature, Math. Res. Lett. 16 (2009), No. 6, 935-939.


(12) Qi S. Zhang and Meng Zhu, New Volume Comparison results and Applications to degeneration of Riemannian metrics, arXiv:1605.09420, 2016


(13) Chenxu He and Meng Zhu, Ricci solitons on Sasakian manifolds, arXiv:1109.4407, 2011

Recent Publications(From MathSciNet)
MR4911667 Reviewed Song, XingYu; Wu, Ling; Zhu, Meng Heat kernel bounds and Cheng-Yau type estimate for the Laplace-Beltrami operator with Bakry-Émery Ricci curvature lower bound. J. Differential Equations 440 (2025), part 2, Paper No. 113439, 51 pp. (Reviewer: Sujit Bhattacharyya) 58J35 (53C21)
Publication Year 2025 Indexed 2025-07-18 Review Published2025-11-10
MR4840277 Reviewed Song, Xingyu; Wu, Ling; Zhu, Meng A direct approach to sharp Li-Yau estimates on closed manifolds with negative Ricci lower bound. Proc. Amer. Math. Soc. 153 (2025), no. 1, 291–305. (Reviewer: Yu Zheng) 53C21 (53E20 58J35)
Publication Year 2025 Indexed 2025-02-25 Review Published2026-02-27
MR4801845 Reviewed Cao, Huai-Dong; Zhu, Meng Linear stability of compact shrinking Ricci solitons. Math. Ann. 390 (2024), no. 2, 2973–2989. (Reviewer: Seungsu Hwang) 53C25 (58E15)
Publication Year 2024 Indexed 2024-11-14 Review Published2025-04-10
MR4706923 Reviewed Wu, Ling; Song, XingYu; Zhu, Meng Eigenvalue estimates for Beltrami-Laplacian under Bakry-Émery Ricci curvature condition. Potential Anal. 60 (2024), no. 2, 597–614. (Reviewer: Feng-Yu Wang) 58C40 (53C21)
Publication Year 2024 Indexed 2024-04-12 Review Published2024-10-31
MR4646817 Reviewed Song, Xingyu; Wu, Ling; Zhu, Meng Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications. J. Geom. Phys. 194 (2023), Paper No. 104997, 28 pp. (Reviewer: Yu Zheng) 58J35 (53C21)
Publication Year 2023 Indexed 2023-11-14 Review Published2024-09-27
MR4303920 Reviewed Lu, Zhiqin; Zhang, Qi S.; Zhu, Meng Gradient and eigenvalue estimates on the canonical bundle of Kähler manifolds. J. Geom. Anal. 31 (2021), no. 10, 10304–10335. (Reviewer: Teng Fei) 53C55 (32Q15 58J35)
Publication Year 2021 Indexed 2021-10-14 Review Published2022-05-26
MR3975707 Reviewed Zhang, Qi S.; Zhu, Meng New volume comparison results and applications to degeneration of Riemannian metrics. Adv. Math. 352 (2019), 1096–1154. (Reviewer: Gang Liu) 53C23 (53C21)
Publication Year 2019 Indexed 2019-08-27 Review Published2019-11-15
MR3969422 Reviewed Zhang, Qi S.; Zhu, Meng Bounds on harmonic radius and limits of manifolds with bounded Bakry-Émery Ricci curvature. J. Geom. Anal. 29 (2019), no. 3, 2082–2123. (Reviewer: Shouhei Honda) 53C21 (53C23)
Publication Year 2019 Indexed 2019-08-26 Review Published2020-03-05
MR3802491 Reviewed Zhang, Qi S.; Zhu, Meng Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions. J. Funct. Anal. 275 (2018), no. 2, 478–515. (Reviewer: Yu-Zhao Wang) 58J35 (53C21)
Publication Year 2018 Indexed 2018-07-20 Review Published2020-01-03
MR3765564 Reviewed Cao, Huai-Dong; Zhu, Meng Aronson-Bénilan estimates for the fast diffusion equation under the Ricci flow. Nonlinear Anal. 170 (2018), 258–281. 35K57 (35K59)
Publication Year 2018 Indexed 2018-04-19 Review Published2018-05-01
MR3637958 Reviewed Zhang, Qi S.; Zhu, Meng Li-Yau gradient bound for collapsing manifolds under integral curvature condition. Proc. Amer. Math. Soc. 145 (2017), no. 7, 3117–3126. (Reviewer: Yi Li) 53C44 (53C21)
Publication Year 2017 Indexed 2017-06-16 Review Published2018-04-02
MR3573121 Reviewed Zhu, Meng On the relation between Ricci-harmonic solitons and Ricci solitons. J. Math. Anal. Appl. 447 (2017), no. 2, 882–889. (Reviewer: Gurupadavva Ingalahalli) 53C44 (35C08 35R01 53C25)
Publication Year 2017 Indexed 2017-01-30 Review Published2017-06-23
MR3449222 Reviewed Zhu, Meng Davies type estimate and the heat kernel bound under the Ricci flow. Trans. Amer. Math. Soc. 368 (2016), no. 3, 1663–1680. (Reviewer: Oliver C. Schnürer) 53C44 (58J35)
Publication Year 2016 Indexed 2016-04-19 Review Published2017-01-13
MR3394614 Reviewed Cao, Huai-Dong; Zhu, Meng Aronson-Bénilan estimates for the porous medium equation under the Ricci flow. J. Math. Pures Appl. (9) 104 (2015), no. 4, 729–748. (Reviewer: James Alexander McCoy) 53C44 (35B45 35B65 35K59 58J35)
Publication Year 2015 Indexed 2015-11-18 Review Published2016-04-18
MR3047191 Thesis Zhu, Meng On stability and rigidity of gradient Ricci solitons. Thesis (Ph.D.)–Lehigh University. 2012. 76 pp. ISBN: 978-1267-37375-5, ProQuest LLC
Publication Year 2012 Indexed 2013-04-29
MR2944741 Reviewed Chen, Qiang; Zhu, Meng On rigidity of gradient Kähler-Ricci solitons with harmonic Bochner tensor. Proc. Amer. Math. Soc. 140 (2012), no. 11, 4017–4025. (Reviewer: Jeffrey Jauregui) 53C25 (53C55)
Publication Year 2012 Indexed 2012-11-07 Review Published2013-02-14
MR2923948 Reviewed Cao, Huai-Dong; Zhu, Meng On second variation of Perelman's Ricci shrinker entropy. Math. Ann. 353 (2012), no. 3, 747–763. (Reviewer: Esther Cabezas Rivas) 53C44
Publication Year 2012 Indexed 2012-10-17 Review Published2013-07-30
MR2811045 Reviewed Zhu, Meng The second variation of the Ricci expander entropy. Pacific J. Math. 251 (2011), no. 2, 499–510. (Reviewer: Manuel Fernández-López) 53C44 (53C21 53C25)
Publication Year 2011 Indexed 2011-10-28 Review Published2012-03-21
MR2576682 Reviewed Cao, Huai-Dong; Zhu, Meng A note on compact Kähler-Ricci flow with positive bisectional curvature. Math. Res. Lett. 16 (2009), no. 6, 935–939. (Reviewer: Zhou Zhang) 53C44 (53C25)
Publication Year 2009 Indexed 2010-03-31 Review Published2010-09-02

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