Yuan Zhang

Yuan Zhang

Professor

Department of Mathematical Sciences
Purdue University Fort Wayne
2102 E. Coliseum Blvd
Fort Wayne, IN 46805, USA

Office: Kettler Hall 268 Phone: 260-481-0340 Email: zhangyu at pfw dot edu

Education:

Ph. D. in Mathematics at Rutgers University. 2009.

B. S. in Mathematics at Wuhan University, China. 2002.

Research:

Several Complex Variables
Partial Differential Equations
CR Geometry

Publications:

Pan, Y. and Zhang, Y., Continuous Sobolev functions with singularity on arbitrary real-analytic sets. Pacific Journal of Mathematics, to appear. pdf
Pan, Y. and Zhang, Y., Optimal Sobolev regularity of $\bar\partial$ on the Hartogs triangle. Mathematische Annalen, to appear. pdf
Zhang, Y., Optimal $L^p$ regularity for $\bar\partial$ on the Hartogs triangle. Journal of Geometric Analysis, 34(2024), no. 9, Paper No. 276, 15 pp. pdf
Zhang, Y., Sobolev regularity of the canonical solutions to $\bar\partial$ on product domains. Comptes Rendus Mathematique, 362(2024), 171–176. pdf
Pan, Y. and Zhang, Y., Weighted Sobolev estimates of the truncated Beurling operator. Bulletin of the London Mathematical Society, 56(2024), no. 1, 232–239.pdf
Pan, Y. and Zhang, Y., Unique continuation for $\bar\partial$ with square-integrable potentials. New York Journal of Mathematics, 29(2023), 402–416. pdf
Dong, X., Treuer, J. and Zhang, Y., Rigidity theorems by capacities and kernels. International Mathematics Research Notices, IMRN(2023), no. 24, 21180–21214. pdf
Liu, Y., Pan, Y. and Zhang, Y., A derivative formula for the solid Cauchy integral operator and its applications. Integral Equations and Operator Theory, 94(2022), no. 4, Paper No. 38. pdf
Fassina, M., Pan, Y. and Zhang, Y., A remark on optimal data spaces for classical solutions of $\bar\partial$. Rocky Mountain Journal of Mathematics, 52(2022), no.2, 499-506. pdf
Zhang, Y., Optimal Hölder regularity for the $\bar\partial$ problem on product domains in $\mathbb C^2$. Proceedings of the AMS, 150(2022), 2937-2943. pdf
Pan, Y. and Zhang, Y., Cauchy singular integral operator with parameters in Log-Hölder spaces. Journal d'Analyse Mathématique, 145(2021), no. 1, 357-379. pdf
Pan, Y. and Zhang, Y., Hölder estimates for the $\bar\partial$ problem for $(p.q)$ forms on product domains. International Journal of Mathematics, 32(2021), no. 3, 20 pp. pdf
Pan, Y. and Zhang, Y., A residue-type phenomenon and its applications to higer order nonlinear systems of Poisson type. Journal of Mathematical Analysis and Applications, 495(2021), no. 2, 30 pp. pdf
Coffman, A. and Zhang, Y., Vector Fields with continuous curl but discontinuous partial derivatives. The American Mathematical Monthly, (10)127(2020), 911-917. pdf
Yin, W., Yuan, Y. and Zhang, Y., The CR immersion into a sphere with the degenerate CR Gauss map. Journal of Geometric Analysis, 30(2020), no. 1, 526-550. pdf
Coffman, A., Pan, Y. and Zhang, Y., Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates. Transactions of the AMS, 369(2017), no. 7, 4865-4887. pdf
Yuan, Y. and Zhang, Y., CR submanifolds with vanishing CR second fundamental forms. Geometriae Dedicata, 183(2016), 169-180. pdf
Huang, X. and Zhang, Y., On the CR transversality of holomorphic maps into hyperquadrics. Abel Symposia, dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthday, 10(2015), Springer, 139-155. pdf
Fornaess, J. E., Lee, L. and Zhang, Y., Formal complex curves in real smooth hypersurfaces. Illinois Journal of Mathematics, 58(2014), no. 1, 1-10. pdf
Lebl, J., Minor, A., Shroff, R., Duong, S. and Zhang, Y., CR singular images of generic submanifolds under holomorphic maps. Arkiv fӧr Matematik, 52(2014), no. 2, 301-327. pdf
Huang, X. and Zhang, Y., On a CR transversality problem through the approach of the Chern-Moser theory. Journal of Geometric Analysis, 23(2013), no. 4, 1780-1793. pdf
Yuan, Y. and Zhang, Y., Rigidity for local holomorphic conformal embeddings from B^n into B^{N_1}×...×B^{N_m}. Journal of Differential Geometry, 90(2012), no. 2, 329-349. pdf
Fornaess, J. E., Lee, L. and Zhang, Y., On supnorm estimates for $\bar\partial$ on infinite type convex domains in $\mathbf C^2$. Journal of Geometric Analysis, 21(2011), no. 3, 495-512. pdf
Faran, J., Huang, X., Ji, S. and Zhang, Y., Polynomial and rational maps between balls, Pure and Applied Mathematics Quarterly 6(2010), no. 3. a special issue in honor of Professor J. Kohn, Part 1, 829-842. pdf
Huang, X. and Zhang, Y., Monotonicity for the Chern-Moser-Weyl curvature tensor and CR embeddings, Sciences in China A, a special issue in honor of Professor Tong-De Zhong, 52(2009). no. 12, 2617-2627. pdf
Ji, S. and Zhang, Y., Classification of rational holomorphic maps from B^2 into B^N with degree 2, Sciences in China A, a special issue in honor of Professor Tong-De Zhong, 52(2009), no. 12, 2647-2667. pdf
Zhang, Y., Rigidity and Holomorphic Segre transversality for holomorphic Segre maps. Mathematische Annalen, 337 (2007), no. 2, 457-478. pdf

Preprints:

Pan, Y. and Zhang, Y., Unique continuation of Schr\"odinger-type equations for $\bar\partial$ II. pdf
Pan, Y. and Zhang, Y., Unique continuation of Schr\"odinger-type equations for $\bar\partial$. pdf
Coffman, A., Pan, Y. and Zhang, Y., Unique continuation for a gradient inequality with $L^n$ potential. pdf
Gryc, W., Lanzani, L., Xiong, J. and Zhang, Y., Boundary value problems for holomorphic functions on Lipschitz planar domains. pdf
Gryc, W., Lanzani, L., Xiong, J. and Zhang, Y., New properties of holomorphic Sobolev-Hardy spaces. pdf
Pan, Y. and Zhang, Y., On solutions to $-\Delta u = V u$ near infinity. pdf
Yuan, Y. and Zhang, Y., Weighted Sobolev estimates of $\bar\partial$ on domains covered by polydiscs. pdf
Dong, X., Pan, Y. and Zhang, Y., Uniform estimates for the canonical solutions to the $\bar\partial$-equation on product domains. pdf