2 citations · 3 across the 10 of their papers we have counts for
10 papers
Closed mean curvature flows with prescribed tangent flows
Jingwen Chen, Tang-Kai Lee, Ao Sun +1
Given an embedded shrinker in that is either closed, asymptotically conical, or a Cartesian product of such a shrinker with , we construct a cl…
On the rate of convergence of cylindrical singularity in mean curvature flow
Yiqi Huang, Xinrui Zhao
We prove that if a rescaled mean curvature flow is a global graph over the round cylinder with small gradient and converges super-exponentially fast, then it must coincide with the…
Enhanced Robotic Navigation in Deformable Environments using Learning from Demonstration and Dynamic Modulation
Lingyun Chen, Xinrui Zhao, Marcos P. S. Campanha +4
This paper presents a novel approach for robot navigation in environments containing deformable obstacles. By integrating Learning from Demonstration (LfD) with Dynamical Systems (…
Closed mean curvature flows with asymptotically conical singularities
Tang-Kai Lee, Xinrui Zhao
In this paper, we prove that for any asymptotically conical self-shrinker, there exists an embedded closed hypersurface such that the mean curvature flow starting from it develops…
Margulis Lemma on spaces
Qin Deng, Jaime Santos-Rodríguez, Sergio Zamora +1
We extend the Margulis Lemma for manifolds with lower Ricci curvature bounds to the setting. As one of our main tools, we obtain improved regularity estimates for…
Uniqueness of conical singularities for mean curvature flows
Tang-Kai Lee, Xinrui Zhao
In this paper, we prove the uniqueness of asymptotically conical tangent flows in all codimensions. This is based on an early work of Chodosh-Schulze, who proved the uniqueness in…
Unique Continuation Problem on RCD Spaces. I
Qin Deng, Xinrui Zhao
In this note we establish the weak unique continuation theorem for caloric functions on compact spaces and show that there exists an space on which there exis…
Failure of strong unique continuation for harmonic functions on RCD Spaces
Qin Deng, Xinrui Zhao
Unique continuation of harmonic functions on space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish th…
A New Definition of the Dimension of Graphs
X. Zhao
Enlighted by the recent work of Hao Huang on sensitivity conjecture [arXiv:1907.00847], we propose a new definition of the dimension of graphs and establish a relationship between…
Review of the Siu-Yang Conjecture
X. Zhao
In this paper we review the development and recent results of the Siu-Yang conjecture which is that every Kähler-Einstein compact complex manifold of complex dimension two with neg…