Jie Zhou

activity

20232026

collaborators

7 papers

math.DG2026

Counterexamples to prescribed scalar curvature in the null case

Yuxiang Li, Yunqing Wu, Jie Zhou

We construct smooth functions on the flat torus $T^{n \geq 5}$ that change sign and have negative mean but cannot be realized as the scalar curvature of any metric in the giv…

math.DG2026

Linear Quantitative Rigidity for Almost-CMC Surfaces

Yuchen Bi, Jie Zhou

We prove a quantitative rigidity result for almost constant mean curvature spheres in $R^{3}$ . Under a sub--two--sphere Willmore bound and a small $L^{2}$ --CMC defect, we show…

math.DG2025

Quantitative Stability of the Clifford Torus as a Willmore Minimizer

Yuchen Bi, Jie Zhou

For an integral $2$ -varifold $V \subset S^{3}$ with square-integrable mean curvature, unit density, and support of genus at least $1$ , assume that its Willmore energy satisfi…

math.DG2024

3-circle Theorem for Willmore surfaces II--degeneration of the complex structure

Yuxiang Li, Hao Yin, Jie Zhou

We study the compactness of Willmore surfaces without assuming the convergence of the induced complex structures. In particular, we compute the energy loss in the neck in terms of…

math.DG2024

Optimal rigidity estimates for varifolds almost minimizing the Willmore energy

Yuchen Bi, Jie Zhou

For an integral $2$ -varifold $V = v (Σ, θ_{\geq 1})$ in $R^{n}$ with generalized mean curvature $H \in L^{2}$ such that $μ (R^{n}) = 4 π$ and $\int_Σ|H|^2dμ\le 16π(1+…

math.CV2023

Gromov-Witten Generating Series of Elliptic Curves and Iterated Integrals of Eisenstein-Kronecker Forms

Jie Zhou

We compute various types of iterated integrals of Eisenstein-Kronecker forms that are constructed from the Kronecker theta function. Furthermore, we relate the generating series of…

math.NT2023

Modularity of counting functions of convex planar polygons with rationality conditions

Kathrin Bringmann, Jonas Kaszian, Jie Zhou

We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms co…