Yuan Yuan's research centers on Several Complex Variables. He has been working on various related geometric, analytical problems, including the rigidity of holomorphic maps, the Bergman and Szegő projections, the ∂¯-equation, and the geometric flows onKählermanifolds.
1) Xiaoliang Cheng, Yihong Hao, Yuan Yuan, Xu Zhang, Local holomorphic isometries from the complex unit ball into product of complex unit balls - negative isometric constants, Mathematische Annalen 391 (2025), no. 4, 6187–6203.
2) Liwei Chen, Steve Krantz, Yuan Yuan, Lp regularity of the Bergman Projection on domains covered by the polydisk, Journal of Functional Analysis 279 (2020), no. 2, 108522.
3) Ming Xiao, Yuan Yuan, Holomorphic maps from the complex unit ball to type IV classical domains, Journal de Mathématiques Pures et Appliquées (9) 133 (2020), 139-166.
4) Yuan Yuan, Local holomorphic isometries, old and new results, Proceedings of the Seventh International Congress of Chinese Mathematicians, Vol. II, 409-422, Somerville, MA: International Press, 2019.
5) Xiaojun Huang, Yuan Yuan, Holomorphic isometry from a Kähler manifold into a product of complex projective manifolds, Geometric and Functional Analysis 24 (2014), no. 3, 854-886.
6) Yuan Yuan, Yuan Zhang, Rigidity for local holomorphic isometric embeddings from Bn into BN1 × · · · × BNm up to conformal factors, Journal of Differential Geometry 90 (2012), no. 2, 329-349.
7) Jian Song, Yuan Yuan, Metric flips with Calabi ansatz, Geometric and Functional Analysis 22 (2012), no. 1, 240-265.