中文摘要：

简要综述了生物膜力学与几何的新进展．在生物膜力学中，着重介绍了基于微分算子的平衡理论和几何约束理论；在生物膜几何中，重点评述了源于生物膜力学的新梯度算子及其积分性质．指出：新梯度算子可能在生物膜曲面上诱发新的驱动力；生物膜力学与几何是一个有机整体，其背后存在着一个对称的几何体系，包括对称的微分算子以及对称的积分定理系统

英文摘要：

This paper briefly reviews the recent progress in the mechanics and geometry for biomembranes. In biomembrane mechanics, the equilibrium theory and geometrically constraint theory are introduced. In biomembrane geometry, a new gradient operator derived from biomembrane mechanics and its integral characteristics are summarized. The new gradient operator may be responsible for a new driving force on biomembrane surfaces. Besides, the mechanics and geometry for biomembranes are found to be an organic entity, behind which is a symmetric geometric system, including symmetric differential operators and symmetric integral theorems.