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19 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…
Uniqueness of conformal-harmonic maps on locally conformally flat 4-manifolds
Longzhi Lin, Jingyong Zhu
Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds and were introduced in search of a natural notion…
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…
Conformal Ricci flow on asymptotically hyperbolic manifolds
Peng Lu, Jie Qing, Yu Zheng
In this article we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds. We also prove a local Shi's type curvature derivative estimate for…
Hypersurfaces with nonnegative Ricci curvature in hyperbolic space
Vincent Bonini, Shiguang Ma, Jie Qing
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymp…