积分流的奇异（Lipschitz）同调和同调

A Formula For the Homology Groups of the Milnor Fibres of an Isolated Real Hypersurface Singularity

Given a nonconstant polynomial map over the reals having an isolated critical point in the origin and with zero locus of positive dimension, we establish a formula for the singular homology groups of a Milnor fibre relative to its boundary.

具有小奇异集的Lipschitz度量的正质量定理

A positive mass theorem for Lipschitz metrics with small singular sets

我们证明了正质量定理适用于Lipschitz度量，只要奇异集是低维的，没有其他条件的奇异集。更精确地说，令$g$是光滑流形$M^n$上的渐近平坦Lipschitz度量，使得$n<8$或$M$是自旋的。只要$g$在某个Minkowski维数小于$n/2$的奇异集$S$的补集上具有有界$C^2$范数和非负数量曲率，则$g$的质量一定非负.我们猜想$S$的维数只需要小于$n-1$，结果就成立。这些结果与H. Bray，P. Miao，and Y. Shi和L.- F.其中$S$是超曲面。

标量曲率在奇数维奇异流形上的Lipschitz刚性

Lipschitz rigidity for scalar curvature on singular manifolds in odd dimensions

本文研究标量曲率在奇数维奇异流形上的Lipschitz刚性，结合谱流论证和抽象锥算子分析，证明了奇数维Riemannian spin流形的刚性结果。

抽象锥算子和奇异流形上数量曲率的Lipschitz刚性

Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

本文利用扭曲Dirac算子的指标理论，证明奇异流形上数量曲率的Llarull型比较结果，并将Lipschitz刚性从偶数维推广到奇数维。

具有锥奇异的子流形的全局 Lipschitz 几何及其在代数集中的应用

Global Lipschitz geometry of conic singular sub-manifolds with applications to algebraic sets

本文证明了黎曼流形中连通的锥奇异子流形是 Lipschitz 正常嵌入的，并利用单点紧化下的闭包等价条件，推导出一般仿射实与复代数集的连通分支在无穷远处呈锥形且满足该嵌入性质。

奇异簇上函数芽的双李普希茨平凡性

Bi-Lipschitz triviality of function-germs on singular varieties

本文研究奇异簇上解析函数芽形变的双李普希茨平凡性，引入强有理双李普希茨平凡族概念并给出无穷小判别准则，进而得到齐次与加权齐次情形下的平凡性和刚性结果。

Approximations of Lipschitz maps via Ehresmann fibrations and Reeb's sphere theorem for Lipschitz functions

We show, as our main theorem, that if a Lipschitz map from a compact Riemannian manifold $M$ to a connected compact Riemannian manifold $N$, where $\dim M \geq \dim N$, has no singular points on $M$ in the sense of F.H. Clarke, then the map admits a smooth approximation via Ehresmann fibrations. We also show the Reeb sphere theorem for Lipschitz functions, i.e., if a closed Riemannian manifold admits a Lipschitz function with exactly two singular points in the sense of Clarke, then the manifold is homeomorphic to the sphere.

On Isolated Real Singularities I

This article and its successor concern the topology of real isolated hypersurface singularities. We prove that after attaching a certain number of handles the real Milnor fibres become contractible, with each handle corresponding to a critical point of a morsification; in particular one recovers the classical formula of Khimshiashvili for the Euler characteristic of the Milnor fibres. We then give sufficient conditions for having that the integer homology groups of the real Milnor fibres are isomorphic to the homology groups of a bouquet of spheres. This is followed by a discussion on real van…