11 papers · 1 filter
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…
Unique continuation for at infinity
Yifei Pan, Yuan Zhang
Motivated by Landis's conjecture on unique continuation at infinity for the Laplacian, we study the corresponding property for the Cauchy-Riemann operator. We prove that every weak…
Constructing bounded pseudoconvex domains of finite D'Angelo type with prescribed weak loci
Martino Fassina, Yifei Pan, Yuan Zhang
We construct smoothly bounded pseudoconvex or convex domains in whose weakly pseudoconvex loci realize prescribed closed sets.
Non-quadratic solutions to the Monge-Ampère equation
Yifei Pan, Yuan Zhang
We construct ample smooth strictly plurisubharmonic non-quadratic solutions to the Monge-Ampère equation on either cylindrical type domains or the whole complex Euclidean space $\m…
On homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates
Liding Yao, Yuan Zhang
We construct homotopy formulae for forms on the product domain , where each…
Unique continuation of Schrödinger-type equations for II
Yifei Pan, Yuan Zhang
In this paper, we extend our earlier unique continuation results \cite{PZ2} for the Schrödinger-type inequality on a domain in by removin…