18 citations · 92 across the 14 of their papers we have counts for
14 papers
Nonnegative Ricci curvature, splitting at infinity, and first Betti number rigidity
Jiayin Pan, Zhu Ye
We study the rigidity problems for open (complete and noncompact) -manifolds with nonnegative Ricci curvature. We prove that if an asymptotic cone of properly contains a Euc…
The Grushin hemisphere as a Ricci limit space with curvature
Jiayin Pan
The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere with such tha…
Singular Weyl's law with Ricci curvature bounded below
Xianzhe Dai, Shouhei Honda, Jiayin Pan +1
We establish two surprising types of Weyl's laws for some compact /Ricci limit spaces. The first type could have power growth of any order (bigger than one). Th…
Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions
Jiayin Pan, Guofang Wei
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 op…
Nonnegative Ricci curvature, metric cones, and virtual abelianness
Jiayin Pan
Let be an open -manifold with nonnegative Ricci curvature. We prove that if its escape rate is not and its Riemannian universal cover is conic at infinity, that is, ev…
Examples of Ricci limit spaces with non-integer Hausdorff dimension
Jiayin Pan, Guofang Wei
We give the first examples of collapsing Ricci limit spaces on which the Hausdorff dimension of the singular set exceeds that of the regular set; moreover, the Hausdorff dimension…
Some topological results of Ricci limit spaces
Jiayin Pan, Jikang Wang
We study the topology of a Ricci limit space , which is the Gromov-Hausdorff limit of a sequence of complete -manifolds with . Our fi…
Nonnegative Ricci curvature and escape rate gap
Jiayin Pan
Let be an open -manifold of nonnegative Ricci curvature and let . We show that if has escape rate less than some positive constant , that is, minimal r…
The Fundamental Groups of Open Manifolds with Nonnegative Ricci Curvature
Jiayin Pan
We survey the results on fundamental groups of open manifolds with nonnegative Ricci curvature. We also present some open questions on this topic.
On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature
Jiayin Pan
A consequence of the Cheeger-Gromoll splitting theorem states that for any open manifold of nonnegative Ricci curvature, if all the minimal geodesic loops at that repre…
Semi-local simple connectedness of non-collapsing Ricci limit spaces
Jiayin Pan, Guofang Wei
Let be a non-collapsing Ricci limit space and let . We show that for any , there is such that every loop in is contractible in , wher…
Ricci curvature and isometric actions with scaling nonvanishing property
Jiayin Pan, Xiaochun Rong
In the study manifolds of Ricci curvature bounded below, a stumbling obstruction is the lack of links between large-scale geometry and small-scale geometry at a fixed reference poi…
Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups
Jiayin Pan
We study the fundamental group of an open -manifold of nonnegative Ricci curvature. We show that if there is an integer such that any tangent cone at infinity of the Rie…
A Proof of Milnor conjecture in dimension 3
Jiayin Pan
We present a proof of Milnor conjecture in dimension 3 based on Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature bounded below. It is different from [Liu] t…