几何分析中的若干不等式与刚性现象

In this program, we will compute the Yamabe invariant of the real projective spaces, which is a special case of R. schoen conjecture; we will also consider the Penrose-type inequality for quasi-local mass; we will discuss the positive mass theorem and Sobolev-type inequalities for Paneitz–Branson operator; Finally, we will compute or estimate the constants in these Sobolev-type inequalities used by geometric analysists.

在本项目中，我们将计算高维数实射影空间的Yamabe不变量，这是R. Schoen猜想的一个特例；我们也将研究拟局部质量的Penrose型不等式；我们将研究Paneitz–Branson算子的正质量定理和Sobolev型不等式；最后，我们将研究几何分析中尤其有用的诸多Sobolev型不等式中的常数。