Author

D. Zhong

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Preprint Sep 2026

Monotone Sobolev functions: approximation, critical points, and level sets

We give an affirmative answer to the planar local smoothing problem in Question~1.7 of D.~Ntalampekos and positive and negative answers to the basic approximation and level-set parts of his higher-dimensional Question~1.8. In every dimension $n\ge2$, each continuous Lebesgue monotone function in $W^{1,p}$ on a bounded...

De-Guang Zhong · 0 citations

Review Aug 2026

Global convergence and monotonicity of Newton iteration for the inverse Gr\"otzsch modulus

Let \[ \mu(r)=\frac{\pi}{2}\frac{\Kc(r')}{\Kc(r)}, \qquad r'=\sqrt{1-r^2},\qquad 0<r<1, \] be the Gr\"otzsch modulus function. Problems 3.38(a)--(b) in a survey of Vuorinen ask whether Newton's iteration for $\mu^{-1}(y)$, initialized by $x_0=1/\cosh y$, converges for every $y>\pi/2$, and whether it is strictly increas...

D. Zhong · 0 citations