中文摘要：

曲面物理和力学中有两个独立的基本微分算子（即“基本微分算子对”）．本文综述如下主题：在所有的基本微分算子对中，经典梯度V（…）和形状梯度 （…）的配对 ，守口是最佳的．具体内容包括：（1）基本微分算子对的形式并不唯一；（2）内积的可交换性确立了 ，审口优于其他基本微分算子对的“最佳”地位；（3）基于 ，守口可以最佳地构造曲面物理和力学的高阶标量微分算子，因而 ，审口是构造曲面物理和力学微分方程的最佳“基本砖块”：（4） ，审口在软物质曲面物理和力学中普遍存在．

英文摘要：

There are two independent fundamental differential operators （called the ＂fundamental differential operator pair＂） on curved surfaces. This paper focuses on the topic： Among all fundamental differential operator pairs, , formed by the classical gradient （…） and the shape gradient （...）, is the optimal one. The following conclusions are included： （1） The paths for constructing the fundamental differential operator pairs are not unique. （2） The commutative nature of the inner-product of is the basis of its optimality and advantage over all other fundamental differential operator pairs. （3） Based on the inner-product of~ , all higher order scalar differential operators for physics and mechanics on curved surfaces can be constructed optimally. In other words, is the optimal ＂fundamental brick＂ for establishing the differential equations of physics and mechanics on curved surfaces. （4） exists universally in physics and mechanics on soft matter curved surfaces.