Jianchun Chu (楚健春)

Publications and Preprints

• (with Y. Liu and N. McCleerey) The Eigenvalue Problem for the Complex Hessian Operator on m-Pseudoconvex Manifolds
  [arxiv] preprint, arXiv: 2402.03098.
  
  
• (with F. Wang and K. Zhang) The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
  [arxiv] preprint, arXiv: 2401.15830.
  
  
• (with S. Chen and J. Zhu) Positive scalar curvature metric and aspherical summands
  [arxiv] preprint, arXiv: 2312.04698.
  
  
• (with S. Dinew) Liouville theorem for a class of Hessian equations
  [arxiv] preprint, arXiv: 2306.13825.
  
  
• (with J. Zhu) A non-spin method to the positive weighted mass theorem for weighted manifolds
  [arxiv] preprint, arXiv: 2305.12909.
  
  
• (with M.-C. Lee and J. Zhu) Singular positive mass theorem with arbitrary ends
  [arxiv] preprint, arXiv: 2210.08261.
  
  
• (with K.-K. Kwong and M.-C. Lee) Rigidity on non-negative intermediate curvature
  [arxiv] preprint, arXiv: 2208.12240.
  
  
• (with M.-C. Lee) Hypercritical deformed Hermitian-Yang-Mills equation revisited
  [arxiv] [journal] J. Reine Angew. Math. 801 (2023), 161-172.
  
  
• (with M.-C. Lee) Ricci-Deturck flow from rough metrics and applications
  [arxiv] preprint, arXiv: 2204.05843.
  
  
• (with N. McCleerey) Lelong Numbers of m-Subharmonic Functions Along Submanifolds
  [arxiv] preprint, arXiv: 2204.01963.
  
  
• (with P.-Y. Chan, M.-C. Lee and T.-Y. Tsang) Monotonicity of the p-Green functions
  [arxiv] preprint, arXiv: 2202.13832.
  
  
• (with M.-C. Lee) Kähler tori with almost non-negative scalar curvature
  [arxiv] [journal] Commun. Contemp. Math. 25 (2023), no. 7, Paper No. 2250030, 13 pp.
  
  
• (with L. Huang and J. Zhang) Fully non-linear elliptic equations on compact almost Hermitian manifolds
  [arxiv] [journal] Calc. Var. Partial Differential Equations 62 (2023), no. 3, Paper No. 105, 34 pp.
  
  
• (with M.-C. Lee) Hypercritical deformed Hermitian-Yang-Mills equation
  [arxiv] preprint, arXiv: 2107.13192.
  
  
• (with M.-C. Lee and R. Takahashi) A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation
  [arxiv] to appear in J. Differential Geom.
  
  
• (with M.-C. Lee) On the Hölder estimate of Kähler-Ricci flow
  [arxiv] [journal] Int. Math. Res. Not. IMRN (2023), no. 6, 4932-4951.
  
  
• (with M.-C. Lee) Conformal tori with almost non-negative scalar curvature
  [arxiv] [journal] Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 114, 20 pp.
  
  
• (with N. McCleerey) Fully non-linear degenerate elliptic equations in complex geometry
  [arxiv] [journal] J. Funct. Anal. 281 (2021), no. 9, Paper No. 109176, 45 pp.
  
  
• (with M.-C. Lee and L.-F. Tam) Kähler manifolds and mixed curvature
  [arxiv] [journal] Trans. Amer. Math. Soc. 375 (2022), no. 11, 7925-7944.
  
  
• (with H. Jiao) Curvature estimates for a class of Hessian type equations
  [arxiv] [journal] Calc. Var. Partial Differential Equations 60 (2021), no. 3, Paper No. 90, 18 pp.
  
  
• A simple proof of curvature estimate for convex solution of k-Hessian equation
  [arxiv] [journal] Proc. Amer. Math. Soc. 149 (2021), no. 8, 3541-3552.
  
  
• (with T. C. Collins and M.-C. Lee) The space of almost calibrated (1, 1) forms on a compact Kähler manifold
  [arxiv] [journal] Geom. Topol. 25 (2021), no. 5, 2573-2619.
  
  
• (with N. McCleerey) C^1,1 regularity of geodesics of singular Kähler metrics
  [arxiv] [journal] J. Lond. Math. Soc. (2) 104 (2021), no. 1, 66-96.
  
  
• C^1,1 regularity of degenerate complex Monge-Ampère equations and some applications
  [arxiv] [journal] Anal. PDE 14 (2021), no. 6, 1671-1700.
  
  
• C^1,1 regularity of geodesics in the space of volume forms
  [arxiv] [journal] Calc. Var. Partial Differential Equations 58 (2019), no. 6, Art. 194, 7 pp.
  
  
• (with L. Huang and X. Zhu) The Fu-Yau equation on compact astheno-Kähler manifolds
  [arxiv] [journal] Adv. Math. 346 (2019), 908-945.
  
  
• (with L. Huang and X. Zhu) The Fu-Yau equation in higher dimensions
  [arxiv] [journal] Peking Math. J. 2 (2019), no. 1, 71-97.
  
  
• (with L. Huang and X. Zhu) The 2-nd Hessian type equation on almost Hermitian manifolds
  [arxiv] preprint, arXiv: 1707.04072.
  
  
• (with V. Tosatti and B. Weinkove) C^1,1 regularity for degenerate complex Monge-Ampère equations and geodesics rays
  [arxiv] [journal] Comm. Partial Differential Equations 43 (2018), no. 2, 292-312.
  
  
• (with B. Zhou) Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
  [arxiv] [journal] Sci. China Math. 62 (2019), no. 2, 371-380.
  
  
• (with V. Tosatti and B. Weinkove) On the C^1,1 regularity of geodesics in the space of Kähler metrics
  [arxiv] [journal] Ann. PDE 3 (2017), no. 2, Art. 15, 12 pp.
  
  
• Quantitative stratification of F-subharmonic functions
  [arxiv] [journal] Comm. Anal. Geom. 29 (2021), no. 6, 1335-1389.
  
  
• The parabolic Monge-Ampère equation on compact almost Hermitian manifolds
  [arxiv] [journal] J. Reine Angew. Math. 761 (2020), 1-24.
  
  
• (with V. Tosatti and B. Weinkove) The Monge-Ampère equation for non-integrable almost complex structures
  [arxiv] [journal] J. Eur. Math. Soc. (JEMS) 21 (2019), no. 7, 1949-1984.
  
  
• C^2,α regularities and estimates for nonlinear elliptic and parabolic equations in geometry
  [arxiv] [journal] Calc. Var. Partial Differential Equations 55 (2016), no. 1, Art. 8, 20 pp.
  
  
• The complex Monge-Ampère equation on some compact Hermitian manifolds
  [arxiv] [journal] Pacific J. Math. 276 (2015), no. 2, 369-386.