Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Pan, Jiayin"'
Understanding the relationships between geometry and topology is a central theme in Riemannian geometry. We establish two results on the fundamental groups of open (complete and noncompact) $n$-manifolds with nonnegative Ricci curvature and linear vo
Externí odkaz:
http://arxiv.org/abs/2410.15488
Autor:
Pan, Jiayin, Ye, Zhu
We study the rigidity problems for open (complete and noncompact) $n$-manifolds with nonnegative Ricci curvature. We prove that if an asymptotic cone of $M$ properly contains a Euclidean $\mathbb{R}^{k-1}$, then the first Betti number of $M$ is at mo
Externí odkaz:
http://arxiv.org/abs/2404.10145
Autor:
Pan, Jiayin
For a Gromov-Hausdorff convergent sequence of closed manifolds $M_i^n\overset{GH}\longrightarrow X$ with $\mathrm{Ric}\ge-(n-1)$, $\mathrm{diam}(M_i)\le D$, and $\mathrm{vol}(M_i)\ge v>0$, we study the relation between $\pi_1(M_i)$ and $X$. It was kn
Externí odkaz:
http://arxiv.org/abs/2404.07478
Autor:
Pan, Jiayin
Let $M$ be an open (complete and non-compact) manifold with $\mathrm{Ric}\ge 0$ and escape rate not $1/2$. It is known that under these conditions, the fundamental group $\pi_1(M)$ has a finitely generated torsion-free nilpotent subgroup $\mathcal{N}
Externí odkaz:
http://arxiv.org/abs/2309.01147
Autor:
Pan, Jiayin
The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere $S^{m+n}$ with $Ric\ge 1$ such that its Gromov-Hausdorff limit is the $n$-dimensional Grushin hemisphere
Externí odkaz:
http://arxiv.org/abs/2211.02747
We establish two surprising types of Weyl's laws for some compact $\mathrm{RCD}(K, N)$/Ricci limit spaces. The first type could have power growth of any order (bigger than one). The other one has an order corrected by logarithm similar to some fracta
Externí odkaz:
http://arxiv.org/abs/2208.13962
Autor:
Pan, Jiayin, Wei, Guofang
We give the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This provides counterexamples to a longtime well-known open question whether the Busemann function at a point of an open manifo
Externí odkaz:
http://arxiv.org/abs/2203.15211
Autor:
Xu, Haining, Pan, Jiayin, Ma, Chunfang, Mintah, Benjamin Kumah, Dabbour, Mokhtar, Huang, Liurong, Dai, Chunhua, Ma, Haile, He, Ronghai
Publikováno v:
In Food Chemistry 15 January 2025 463 Part 2
Autor:
Pan, Jiayin
Publikováno v:
Geom. Topol. 28 (2024) 1409-1436
Let $M$ be an open $n$-manifold with nonnegative Ricci curvature. We prove that if its escape rate is not $1/2$ and its Riemannian universal cover is conic at infinity, that is, every asymptotic cone $(Y,y)$ of the universal cover is a metric cone wi
Externí odkaz:
http://arxiv.org/abs/2201.07852
Autor:
Li, Yihe, Xu, Haining, Pan, Jiayin, Mintah, Benjamin Kumah, Dabbour, Mokhtar, He, Ronghai, Ma, Haile
Publikováno v:
In International Journal of Biological Macromolecules December 2024 282 Part 4