4 papers
A Hopf Lemma for Holomorphic Maps into Hyperquadrics
Xiaojun Huang, Yuan Zhang, Weixia Zhu
More than twenty years ago, Baouendi and the first author proved that a holomorphic map between hyperquadrics of the same signature is either totally degenerate or has a nonvanishi…
Semi-classical heat kernel asymptotics on complex manifolds with boundary
Chin-Yu Hsiao, George Marinescu, Weixia Zhu
Let be a relatively compact open subset of a complex manifold with smooth boundary and let be a holomorphic line bundle over . Assuming that condition h…
Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Yahong Yang, Zecheng Zhang, Wei Zhu +2
We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms. In contrast to standard operator-lear…
Heat kernel asymptotics for Kodaira Laplacians of high power of line bundle over complex manifolds
Huan Wang, Weixia Zhu
This paper presents a simple method to prove the heat kernel asymptotics for the Kodaira Laplacian with respect to the high power of a holomorphic Hermitian line bundle o…