18 citations · 92 across the 14 of their papers we have counts for
4 papers · 1 filter
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…