6 citations · 6 across the 4 of their papers we have counts for
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Regularity and structure of spaces with synthetic Ricci bounds and positive injectivity radius
Shouhei Honda, Ruobing Zhang
In the paper, we develop a structure theory for metric measure spaces with synthetic lower Ricci curvature bounds, known as RCD spaces. Under a positive injectivity-radius assumpti…
On the Poincaré-Einstein manifolds with cylindrical conformal infinity
Sun-Yung Alice Chang, Paul Yang, Ruobing Zhang
In this paper, we prove several rigidity and quantitative rigidity results for asymptotically hyperbolic Poincaré-Einstein manifolds whose conformal infinities are diffeomorphic to…
The singular sets of degenerate and nonlocal elliptic equations on Poincaré-Einstein manifolds
Xumin Jiang, Yannick Sire, Ruobing Zhang
The main objects of this paper include some degenerate and nonlocal elliptic operators which naturally arise in the conformal invariant theory of Poincaré-Einstein manifolds. These…
A Liouville theorem on asymptotically Calabi spaces
Song Sun, Ruobing Zhang
In this paper, we will study harmonic functions on the complete and incomplete spaces with nonnegative Ricci curvature which exhibit inhomogeneous collapsing behaviors at infinity.…
Collapsing Ricci-flat metrics on elliptic K3 surfaces
Gao Chen, Jeff Viaclovsky, Ruobing Zhang
For any elliptic K3 surface , we construct a family of collapsing Ricci-flat Kähler metrics such that curvatures are uniformly b…
Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces
Hans-Joachim Hein, Song Sun, Jeff Viaclovsky +1
We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding con…