Optimal Lipschitz Estimates for the $\bar\partial$ equation on a class of convex domains

Lipschitz Estimates for Conformal Maps from the Unit Disk to Convex Domains

We obtain an explicit uniform upper bound for the derivative of a conformal mapping of the unit disk onto a convex domain. This estimate depends only on the outer and inner radii of the domain, and on a curvature radius of its boundary. Its proof is based on a Möbius invariant metric of hyperbolic type, introduced by Kulkarni and Pinkall in 1994.

Sharp Lipschitz estimates for operator $\bar\partial_M$ on a q-pseudoconcave CR manifold

We construct integral homotopy operators on a regular CR manifold and prove sharp estimates for these operators in a special Lipschitz scale.

调和函数与$\barα$-Poisson方程解的Lipschitz连续性

Lipschitz continuity for harmonic functions and solutions of the $\barα$-Poisson equation

该研究探讨平面情形下$\barα$-Poisson方程解的Lipschitz连续性，回顾近期相关成果，并以推论形式重新给出调和函数与梯度调和函数的对应结果。

Lipschitz spaces and harmonic mappings

In \cite{kamz} the author proved that every quasiconformal harmonic mapping between two Jordan domains with $C^{1,α}$, $0<α\le 1$, boundary is bi-Lipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains $Ω_j$, $j=1,2$, with $C^{j,α}$, $j=1,2$ boundary is bi-Lipschitz.

Sharp Lipschitz estimates for operator dbar_M on a q-concave CR manifold

We prove that the integral operators $R_r$ and $H_r$ constructed in \cite{P} and such that $$f = \bar\partial_{\bold M} R_r(f) + R_{r+1}(\bar\partial_{\bold M} f) + H_r(f),$$ for a differential form $f \in C_{(0,r)}^{\infty}({\bold M})$ on a regular q-concave CR manifold ${\bold M}$ admit sharp estimates in the Lipschitz scale.

The d-bar-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in CP^n with n>= 3

A Lipschitz hypersurface is a hypersurface which locally is the graph of a Lipschitz function. A Lipschitz (or C^1) hypersurface is said to be Levi-flat if it is locally foliated by complex manifolds of complex dimension (n-1). We shall prove that there exist no Lipschitz Levi-flat hypersurfaces in CP^n with n >= 3. Our new estimates on the d-bar-Cauchy problems are different from the earlier Siu's integral kernal method.