10 papers
Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia
Graham Denham, Rosa Miró-Roig, Hal Schenck
We construct a rank-9 uniform non-homogeneous vector bundle on . This yields the first counterexample to the longstanding open conjecture that every uniform vector b…
The modified Cartan conjecture
Alexandre Eremenko, Zongben Xu, Teng Zhang
In 1928 H. Cartan stated a conjecture about holomorphic curves in parametrized by the unit disc, omitting hyperplanes in general position. He proved it for $n=…
Sharp tangent inequalities in noncommutative -spaces
Zongben Xu, Teng Zhang
Let be a von Neumann algebra equipped with a faithful normal semifinite weight, and let denote the associated Haagerup noncommutative -space.…
A counterexample to Nevanlinna's century-old half-plane problem
Yixin He, Teng Zhang
Let , and let denote the Nevanlinna class in , consisting of meromorphic functions representable as…
The solution to Kadison's problem on orthonormal bases of unitaries for type factors
Yixin He, Quanyu Tang, Zongben Xu +1
In 1967, Kadison asked whether every type factor admits an orthonormal basis, with respect to its trace, consisting of unitaries. We resolve this problem in full ge…
The separable case of Kadison's problem on orthonormal bases of unitaries for type factors
Yixin He, Quanyu Tang, Teng Zhang
In 1967, Kadison asked ``does every type factor have an orthonormal (with respect to the trace) basis consisting of unitaries?'' Using a noncommutative Lyapunov the…
Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class
Yixin He, Quanyu Tang, Teng Zhang
We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carathéodory class. This resolves a problem of D.~K.~Thomas.
A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions
Yixin He, Quanyu Tang, Teng Zhang
We construct an entire function such that the family of entire functions of \(z\) is normal on…
A rigidity theorem for complex Kleinian groups
Richard Canary, Tengren Zhang, Andrew Zimmer
Farre, Pozzetti and Viaggi proved that any (d-k)-hyperconvex subgroup of PSL(d,C) is virtually isomorphic to a convex cocompact Kleinian group and that its k-th simple root critica…
Geometry and Dynamics of Transverse Groups
Richard Canary, Tengren Zhang, Andrew Zimmer
We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.