Hessian矩阵的若干应用

Applications of Hessian Matrix

介绍了Hessian矩阵在多元向量值函数的极值问题、Morse理论、计算机数值计算和调和映射方面的应用情况.在调和映射方面,提供了用Hessian矩阵刻画水平弱共形映射的完全提升仍然是水平弱共形映射的等价条件,并在证明过程中揭示出Hessian矩阵与齐二次多项式、Nabla算子存在的密切关系.

Hessian matrix is a special form of Jacobian matrix. This matrix form is very useful with a wide application in the following aspects ： extremum problem of vector function with more variables, Morse theory, numerial computation and harmonic map. The harmonic map provides that in character equivalent conditions complete lifting of horizontally weakly conformal maps is also horizontally weakly conformal map, and reveals the close relation between Hessian matrix and homogeneous quadratic polynomial, Nabla operator.