本项目拟研究广义相对论中Einstein约束方程及负宇宙学常数情形超对称紧致化空间上的正质量定理。具体地说，我们将研究以下三个问题：(1)极限方程存在非平凡解时，共形约束系统的可解性。（2）参数微小扰动下，共形协变分裂系统的可解性。（3）渐近于AdS时空与紧致Calabi-Yau 3-流形乘积的空间上的正质量定理。该项目所涉及的问题已成为现代国际数学物理的主流方向之一，具有很高的学术研究价值。我们深信通过自身的努力以及项目的资助，按照研究计划做出有意义且有深度的结果是完全有可能的。

This project aims to investigate the Einstein constraint equations in general relativity and the positive mass theorem for SUSY compactification spaces with negative cosmological constant. Precisely, we are going to study the following three problems: (1) When the limit equation has nontrivial solutions, the solvability of the conformal constraint system. (2) The solvability of the conformal covariant split system under small perturbation of parameters. (3) The positive mass theorem for spaces approaching the product of the AdS spacetime and a Calabi-Yau 3-fold. The above problems are issues in the mainstream of modern mathematical physics and they are with considerable scientific significance. We are confident that, with our efforts, it is very likely that insightful results be achieved if this project is approved.