Let W be the wedge \(\{z: \mathrm {arg}\,z\in (-\pi /4,\pi /4)\}\) in the complex plane \({\mathbb {C}}\) and assume that \({\mathbb {D}}\) is the unit disk. Assume further that \(\Sigma \subset {\mathbb {C}}\times {\mathbb {R}}\) is a minimal surface over W. We obtain some sharp point-wise estimates of Gram–Schmidt norm of the first derivative of a harmonic diffeomorpism of the unit disk onto W. Further we apply this result to obtain some upper estimates of the Gaussian curvature of the minimal surface \(\Sigma \) at a given point Q in term of underlaying point \(w\in W\). This improves some result by Abu-Muhanna and Schober (Can J Math 39(6):1489–1530, 1987).

令W为复平面\（{\ mathbb {C}}中的楔形\（\ {z：\ mathrm {arg} \，z \ in（-\ pi / 4，\ pi / 4）\} \）\）并假定\（{\ mathbb {D}} \）是单位磁盘。进一步假设\（\ Sigma \ subset {\ mathbb {C}} \ times {\ mathbb {R}} \）是W上的最小曲面。我们获得了单位圆盘向W的谐波微分方程的一阶导数的Gram–Schmidt范数的一些尖锐的逐点估计。进一步，我们将这个结果应用到给定点Q上最小点\（\ Sigma \）的高斯曲率的较高估计值，该点的下标点\（w \ in W \）。这改善了Abu-Muhanna和Schober的一些结果（Can J Math 39（6）：1489-1530，1987）。