9 citations · 25 across the 10 of their papers we have counts for
11 papers
The Singular Fibration of Collapsing RCD Spaces with Reifenberg Local Covers
Shaosai Huang
Let compact spaces converge in the measured Gromov--Hausdorff sense, and suppose that they have -Reifenberg local covers for one fixed , with $|κ|ρ^…
The Taub-NUT Metric Is Not Projectively Induced
Shaosai Huang
LeBrun's Kähler realization of the Taub--NUT metric on is complete, Ricci-flat and not flat. Loi, Zedda and Zuddas proved that no multiple admits a Kähl…
Ricci flow smoothing for locally collapsing manifolds
Shaosai Huang, Bing Wang
We show that for certain locally collapsing initial data with Ricci curvature bounded below, one could start the Ricci flow for a definite period of time. This provides a Ricci flo…
Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
Shaosai Huang, Xiaochun Rong, Bing Wang
We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and th…
Rigidity of the first Betti number via Ricci flow smoothing
Shaosai Huang, Bing Wang
The Colding-Gromov gap theorem asserts that an almost non-negatively Ricci curved manifold with unit diameter and maximal first Betti number is homeomorphic to the flat torus. In t…
Small fiberwise oscillation of the eigenfunctions of collapsing Einstein manifolds
Shaosai Huang, Selin Taskent
By Cheeger-Colding's almost splitting theorem, if a domain in a Ricci flat manifold is pointed-Gromov-Hausdorff close to a lower dimensional Euclidean domain, then there is a harmo…
On the long-time behavior of immortal Ricci flows
Shaosai Huang
For an immortal Ricci flow on an -dimensional closed manifold, we show the following convergence results: (1) if the curvature and diameter are uniformly bounded, the…
Notes on Ricci flows with collapsing initial data (I): Distance distortion
Shaosai Huang
In this note, we prove a uniform distance distortion estimate for Ricci flows with uniformly bounded scalar curvature, independent of the lower bound of the initial -entropy. Ou…
On the regular-convexity of Ricci shrinker limit spaces
Shaosai Huang, Yu Li, Bing Wang
In this paper, we study the structure of the pointed-Gromov-Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeg…
Rigidity of vector valued harmonic maps of linear growth
Shaosai Huang, Bing Wang
Consider vector valued harmonic maps of at most linear growth, defined on a complete non-compact Riemannian manifold with non-negative Ricci curvature. For the norm square of the p…
-Regularity and Structure of 4-dimensional Shrinking Ricci Solitons
Shaosai Huang
A closed four dimensional manifold cannot possess a non-flat Ricci soliton metric with arbitrarily small -norm of the curvature. In this paper, we localize this fact in the ca…