Peking-Westlake Geometric Analysis Seminar (Spring 2025)

This is a Geometric Analysis Seminar held by

  • Prof. Yuguang Shi (Peking University)
  • and Dr. Jintian Zhu (Westlake University).

    • We welcome everyone who is interested in attending our seminar. If you would like to be added in the email list, please tell us by sending an email to zhujintian AT westlake DOT edu DOT cn or haotz AT pku DOT edu DOT cn.

    Our seminar usually lasts 1.5 hours (including one-hour talk and half-hour discussion) but it would be flexible according to the speaker. The seminar will be arranged at

  • (Morning Session) 9:00-10:30 AM, every Friday (Beijing time).

    • The talk will be given online with Tencent Meeting or Zoom (optional if the speaker cannot use Tencent Meeting).

  • Tencent Meeting: 898 3182 7279 Password: 541944 .
  • Zoom: 961 2975 0539 Password: 345386 .

    • The schedule is shown in the following table and you can find the details of the planned talks below this table.

    Week 1 (Sep 12, 9-10:30AM) Week 2 (Sep 19, 9-10:30AM) Week 3 (Sep 26, 9-10:30AM) Week 4 (Oct 3, 9-10:30AM)
    Speaker: Dr. Zetian Yan (严泽田) Speaker: Prof. Hao Yin (殷浩) Speaker: Dr. Shuli Chen (陈淑璃) National Holiday
    Week 5 (Oct 10, 9-10:30AM) Week 6 (Oct 14, 15-16:30PM) Week 7 (Oct 24, 9-10:30AM) Week 8 (Oct 31, 9-10:30AM)
    No Arrangement Speaker: Dr. Mingwei Zhang No Arrangement Speaker: Dr. Zhu Ye (叶铸)
    Week 9 (Nov 7, 9-10:30AM) Week 10 (Nov 14, 9-10:30AM) Week 11 (Nov 21, 9-10:30AM) Week 12 (Nov 28, 9-10:30AM)
    No arrangement Speaker: Dr. Ruojing Jiang (姜若晶) Speaker: Dr. Anushree Das Speaker: Prof. Ye-kai Wang
    Week 13 (Dec 5, 9-10:30AM) Week 14 (Dec 12, 9-10:30AM) Week 15 (Dec 19, 9-10:30AM) Week 16 (Dec 26, 9-10:30AM)
    Speaker: Dr. Mingyang Li Speaker: Dr. Xuwen Zhang (张旭文) Speaker: Prof. Ruobing Zhang Speaker: Zehao Sha
    Week 17 (Jan 2, 9-10:30AM) Week 18 (Jan 9, 9-10:30AM)
    Speaker: Speaker:

    Previous Seminars

  • Spring 2023
  • Autumn 2023
  • Spring 2024
  • Autumn 2024
  • Spring 2025

    • Autumn 2025


    Week 1
    Tencent Meeting: 898 3182 7279 Password: 541944 .

    Speaker: Dr. Zetian Yan (UCSB)

    Title: Rigidity of CMC hypersurfaces in $5$- and $6$-manifolds
    Abstract: We prove that nonnegative $3$-intermediate Ricci curvature combined with uniformly positive $k$-triRic curvature implies rigidity of complete noncompact two-sided stable minimal hypersurfaces in a Riemannian manifold $(X^5,g)$ with bounded geometry. The stonger assumption of nonnegative $3$-intermediate Ricci curvature can be replaced by the nonnegativity of Ricci and biRic curvature. In particular, there is no complete noncompact stable minimal hypersurface in a closed $5$-dimensional manifold with positive sectional curvature. This extends result of Chodosh-Li-Stryker [J. Eur. Math. Soc (2025)] to $5$-dimension. We also establish rigidity results on CMC hypersurfaces with nonzero mean curvature in $5$- and $6$-manifolds.

    Week 2
    Tencent Meeting: 898 3182 7279 Password: 541944 .

    Speaker: Prof. Hao Yin (USTC)

    Title: On coordinates at the infinity of ALE Ricci flat manifolds
    Abstract: In this talk, we discuss coordinates at the infinity of ALE Ricci flat manifold and the expansion of metric tensors. We define a concept of Weyl tensor at the infinity if the $L^{m/2}$ norm of the curvature is finite. We also extend the definition of the renormalized volume due to Biquard and Hein to general dimensions. This is a joint work with Bing Wang.

    Week 3
    Tencent Meeting: 898 3182 7279 Password: 541944 .

    Speaker: Dr. Shuli Chen (UChicago)

    Title: Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay
    Abstract: We prove that if an orientable $3$-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \frac{2}{3}$, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and $S^2\times S^1$ summands. Consequently, $M$ carries a complete Riemannian metric of uniformly positive scalar curvature. The decay constant $\frac{2}{3}$ is sharp, as demonstrated by metrics on $R^2 \times S^1$. This improves a result of Balacheff, Gil Moreno de Mora Sard{\`a}, and Sabourau, and partially answers a conjecture of Gromov. The main tool is a new exhaustion result using $\mu$-bubbles.

    Week 6
    Tencent Meeting: 898 3182 7279 Password: 541944 .

    Speaker: Mingwei Zhang (Wuhan University and Freiburg University)

    Title: Spinorial Sobolev inequalities
    Abstract: In this talk we consider various spinorial Sobolev inequalities. We will talk about the spectral analysis of Dirac operator and prove an improved quantitative inequality. This is a joint work with Prof. Guofang Wang.

    Week 8
    Tencent Meeting: 898 3182 7279 Password: 541944 .

    Speaker: Dr. Zhu Ye (Tsinghua University)

    Title: Volume growth and asymptotic cones of manifolds with nonnegative Ricci curvature
    Abstract: Let $M$ be an open (i.e. complete and noncompact) manifold with nonnegative Ricci curvature. We prove that, under the conic at infinity condition, if the infimum of the volume growth order of $M$ equals $k$, then there exists an asymptotic cone of $M$ whose upper box dimension is at most $k$. We also extend or partially extend Sormani's results concerning $M$ with linear volume growth to more relaxed volume growth conditions.

    Week 10
    Zoom: 961 2975 0539 Password: 345386 .

    Speaker: Dr. Ruojing Jiang (MIT)

    Title: Stability of Ricci flow and Volume Comparison for Finite-volume Hyperbolic $3$-manifolds
    Abstract: In this talk, I will discuss a joint work with Franco Vargas Pallete on finite-volume hyperbolic $3$-manifolds. If the initial metric is close to the hyperbolic metric $g_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $g_0$ in a weighted Holder norm. Furthermore, I will also present an application to volume comparison, which shows that among metrics with scalar curvature bounded below by $-6$, $g_0$ minimizes the volume.

    Week 12
    Zoom: 961 2975 0539 Password: 345386 .

    Speaker: Prof. Yekai Wang (NYCU)

    Title: On the Geometry and Uniqueness of Asymptotically Locally Hyperbolic Static Vacuum Black Holes
    Abstract: The classical Minkowski inequality (1903) gives a sharp lower bound for the total mean curvature of a closed convex surface in Euclidean space. Using inverse mean curvature flow (IMCF), Guan-Li (2007) showed that the Minkowski inequality holds for star-shaped mean-convex surfaces. In 2012, Brendle-Hung -Wang established the Minkowski inequality on anti-de Sitter Schwarzschild space. The key in their proof is a new monotonicity formula based on the Heintze-Karcher inequality. I will discuss a joint work with Brian Harvie in which we generalize the Minkowski inequality to 3-dimensional asymptotically locally hyperbolic static manifolds and use it to obtain some black hole uniqueness theorems.

    Week 14
    Tencent Meeting: 898 3182 7279 Password: 541944 .

    Speaker: Dr. Xuwen Zhang (Freiburg University)

    Title: Anisotropic minimal graphs with free boundary
    Abstract: Minimal surface equation is a classical topic in Geometric Analysis and PDEs. In this talk, we discuss recent progress on anisotropic minimal surface equation, and prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-side linear growth. The linear growth assumption is sharp, in view of the recent examples constructed by Connor Mooney-Yang Yang (The anisotropic Bernstein problem, Invent. Math. 235 (2024), no. 1, 211--232). This is a joint work with Guofang Wang, Wei Wei, and Chao Xia.