3 papers
math.CV2026
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…
math.AP2026
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…
math.CV2026
Quasiregular values from generalized manifold with controlled geometry
Deguang Zhong
The main aim of this paper is to establish the Reshetnyak's theorem for quasiregualr values from generalized -manifold with suitable controlled geometry to Euclidean space $\mat…