7 papers
Odd branching obstructs multiplicity-one integral current structures
Deguang Zhong
Giuliano Basso asked whether every -dimensional integral current space admits an integral current structure with the same characteristic set and multiplicity one almost everywhe…
A counterexample to an open problem of Dorff
Zhi-Gang Wang, Deguang Zhong
The classical Pólya-Schoenberg conjecture, proved by Ruscheweyh-Sheil-Small, asserts that the convolution of two normalized convex univalent functions is again convex. This propert…
Meromorphic solutions of first-order differential equations with rational exponential coefficients
Deguang Zhong, Fanning Meng, Wenjun Yuan
We study first-order differential equations , where $R\in\C(t,w)$. We prove that a meromorphic solution on the whole complex plane is algebraic over $\C(e^z)$ unless $…
Sharp mean-width and Jacobian bounds for Euclidean and hyperbolic harmonic maps
Deguang Zhong, David Kalaj
We prove a sharp mean-width inequality for monotone zonal operators and derive global and differential bounds for Euclidean and hyperbolic-harmonic self-maps of the unit ball. Let…
Global convergence and monotonicity of Newton iteration for the inverse Grötzsch modulus
Deguang Zhong
Let \[ μ(r)=\fracπ{2}\frac{\Kc(r')}{\Kc(r)}, \qquad r'=\sqrt{1-r^2},\qquad 0<r<1, \] be the Grötzsch modulus function. Problems 3.38(a)--(b) in a survey of Vuorinen ask whether New…
A Pogorelov-type counterexample to the discreteness and openness of gradient mappings
Deguang Zhong
Let be a domain, and suppose that satisfies the following ineqiality \[ \det D^2u\geq δ>0\qquad\text{a.e. in }Ω. \] A question of G…