RF

Publication List

 RF


Published/Accepted
  1. Torelli-type theorems for gravitational instantons with quadratic volume growth
    (joint with Gao Chen and Jeff Viaclovsky). To appear in Duke Mathematical Journal (2023) [arXiv]

  2. Hodge theory on ALG$^*$ manifolds
    (joint with Gao Chen and Jeff Viaclovsky). To appear in Journal für die reine und angewandte Mathematik (2023) [arXiv]

  3. Collapsing geometry of of hyperkähler 4-manifolds and applications
    (joint with Song Sun). To appear in Acta Mathematica (2022) [arXiv]

  4. Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface
    (joint with Hans-Joachim Hein, Song Sun, and Jeff Viaclovsky). Journal of the American Mathematical Society, 35(2022), no. 1, 123-209,
    [Journal] [arXiv]

  5. A Liouville theorem on asymptotically Calabi spaces
    (joint with Song Sun). Calculus of Variations and Partial Differential Equations, 60(2021), no. 103, [Journal] [arXiv]

  6. Collapsing Ricci-flat metrics on elliptic K3 surfaces
    (joint with Gao Chen and Jeff Viaclovsky). Communications in Analysis and Geometry, 28(2020), no.8, 2019-2133 [Journal] [arXiv]

  7. Regularity and rigidity for nonlocal curvatures in conformal geometry
    (joint with Wenxiong Chen). Journal of Mathematical Studies, 53(2020), no.4, 436-470 [Journal][Preprint]

  8. A note on the collapsing geometry of hyperkähler four manifolds
    (joint with Shouhei Honda and Song Sun). Science China Mathematics, 62(2019), no. 11, 2195-2210 [Journal] [Preprint]

  9. Nonlocal curvature and topology of locally conformally flat manifolds
    Advances in Mathematics, 335(2018), 130-169. [Journal] [arXiv]

  10. A direct method of moving spheres on fractional order equations
    (joint with Wenxiong Chen and Yan Li). Journal of Functional Analysis, 272(2017), no. 10, 4131-4157 [Journal] [arXiv]

  11. Topology and $\epsilon$-regularity theorems on collapsed manifolds with Ricci curvature bounds
    (joint with Aaron Naber). Geometry and Topology, 20 (2016), no.5, 2575-2664 [Journal] [arXiv]


Preprints
  1. The singular sets of degenerate and nonlocal elliptic equations on Poincaré-Einstein manifolds
    (joint with Xumin Jiang and Yannick Sire). Submitted, 2023 [arXiv]

  2. Asymptotically Calabi metrics and weak Fano manifolds
    (joint with Hans-Joachim Hein, Song Sun, and Jeff Viaclovsky). Submitted, 2023 [arXiv]

  3. Complex structure degenerations and collapsing of Calabi-Yau metrics
    (joint with Song Sun). Submitted, 2019 [arXiv]