紧Spin流形上Dirac-Laplace方程解的存在性

Existence Results for Solutions of a Dirac-Laplace Equation on Compact Spin Manifolds.

本研究利用对称形式的山路定理阐释了紧Spin流形上Dirac-Laplace方程解的存在性,改进了文献[2]中的条件,得到了Dirac-Laplace方程具有无穷多对不同的解,这为高阶Dirac方程解的存在性研究提供了重要的参考.

This paper studies the existence of solutions to Dirac-Laplace equation on a compact spin manifold by using the Mountain road theorem in symmetric form,improves the conditions in reference[2],and finds that the Dirac-Laplace equation has infinitely many different pairs of solutions,which provides an important reference for the study of the existence of higher-order Dirac equation solutions.