24 citations · 82 across the 14 of their papers we have counts for
14 papers
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…
Torelli-type theorems for gravitational instantons with quadratic volume growth
Gao Chen, Jeff Viaclovsky, Ruobing Zhang
We prove Torelli-type uniqueness theorems for both ALG gravitational instantons and ALG gravitational instantons which are of order . That is, the periods uniquely character…
Asymptotically Calabi metrics and weak Fano manifolds
Hans-Joachim Hein, Song Sun, Jeff Viaclovsky +1
We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises f…
Hodge theory on ALG manifolds
Gao Chen, Jeff Viaclovsky, Ruobing Zhang
We develop a Fredholm Theory for the Hodge Laplacian in weighted spaces on ALG manifolds in dimension four. We then give several applications of this theory. First, we show the…
Collapsing geometry of hyperkähler 4-manifolds and applications
Song Sun, Ruobing Zhang
We investigate the collapsing geometry of hyperkähler 4-manifolds. As applications we prove two well-known conjectures in the field. (1) Any collapsed limit of unit-diameter hyperk…
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…
Complex structure degenerations and collapsing of Calabi-Yau metrics
Song Sun, Ruobing Zhang
In this paper, we make progress on understanding the collapsing behavior of Calabi-Yau metrics on a degenerating family of polarized Calabi-Yau manifolds. In the case of a family o…
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…
Non-local Curvature and Topology of Locally Conformally Flat Manifolds
Ruobing Zhang
In this paper, we focus on the geometry of compact conformally flat manifolds with positive scalar curvature. Schoen-Yau proved that its universal cover $(\widetilde{M^n}…
Direct Method of Moving Spheres on Fractional Order Equations
Wenxiong Chen, Yan Li, Ruobing Zhang
In this paper, we introduce a direct method of moving spheres for the nonlocal fractional Laplacian for , in which a key ingredient is the narrow region…
Topology and ε-regularity Theorems on Collapsed Manifolds with Ricci Curvature Bounds
Aaron Naber, Ruobing Zhang
In this paper we discuss and prove -regularity theorems for Einstein manifolds , and more generally manifolds with just bounded Ricci curvature, in the collapsed settin…