Codimension one spheres which are null homotopic

广义Robertson-Walker时空中类光超曲面内的余维二类空子流形

Codimension two spacelike submanifolds into null hypersurfaces of generalized Robertson-Walker spacetimes

本文研究广义Robertson-Walker时空中类光锥内的余维二类空子流形，给出径向坐标条件使其分别共形微分同胚于双曲空间、圆圆柱面或球面，并得到弱俘获子流形的非存在性结果。

The codimension 2 null cut locus with applications to spacetime topology

In this paper we review and extend some results in the literature pertaining to spacetime topology while naturally utilizing properties of the codimension 2 null cut locus. Our results fall into two classes, depending on whether or not one assumes the presence of horizons. Included among the spacetimes we consider are those that apply to the asymptotically (locally) AdS setting.

Minkowski formulae and Alexandrov theorems in spacetime

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimension-two submanifold with constant normalized null expansion (null mean curvature) must lie in a shear-free (umbilical) null hypersurface. These results are generalized for higher order curvature invariants. In particular, the notion of mixed higher order mean curvature is intr…

每个非平坦共形极小曲面都可同伦于一个proper的一个

Every nonflat conformal minimal surface is homotopic to a proper one

论文证明了非平坦共形极小浸入可通过非平坦共形极小浸入同伦于proper的一个，且当n≥5时可选择为injective的proper共形极小嵌入。

Mountain pass energies between homotopy classes of maps

For non-homotopic maps $u,v\in C^{\infty}(M,N)$ between closed Riemannian manifolds, we consider the smallest energy level $γ_p(u,v)$ for which there exist paths $u_t\in W^{1,p}(M,N)$ connecting $u_0=u$ to $u_1=v$ with $\|du_t\|_{L^p}^p\leq γ_p(u,v)$. When $u$ and $v$ are $(k-2)$-homotopic, work of Hang and Lin shows that $γ_p(u,v)<\infty$ for $p\in [1,k)$, and using their construction, one can obtain an estimate of the form $γ_p(u,v)\leq \frac{C(u,v)}{k-p}$. When $M$ and $N$ are oriented, and $u$ and $v$ induce different maps on real cohomology in degree $k-1$, we show that the growth $γ_p(u,…

有界指标极小超曲面奇异集的定量估计

Quantitative Estimates on the Singular Set of Minimal Hypersurfaces with Bounded Index

本文针对满足光滑部分有限指标、奇异集$\u210b^{n-1}$零测的余维1平稳积分n-varifold，证明其奇异集管状邻域局部测度界，改进了相关已知结果并补充奇异集结构信息。