5 papers
Global regularity of Skew mean curvature flow for small data in dimensions
Jiaxi Huang, Ze Li, Daniel Tataru
The skew mean curvature flow is an evolution equation for a dimensional manifold immersed into , and which moves along the binormal direction with a speed pro…
On long time dynamics of 1D Schrödinger map flows
Ze Li
In this paper, we study the long time dynamics of small solutions to Schrödinger map flows from to Riemannian surfaces. The results are threefold. (i) We prove that for ge…
On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps
Ze Li
The results of this paper are twofold: In the first part, we prove that for Schrödinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatur…
Global transversal stability of Euclidean planes under skew mean curvature flow evolutions
Ze Li
In this paper, we prove that 2 dimensional transversal small perturbations of d-dimensional Euclidean planes under the skew mean curvature flow lead to global solutions which conve…
Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: High dimensions
Ze Li
In this paper, we prove that the Schrödinger map flows from with to compact Kähler manifolds with small initial data in critical Sobolev spaces are global. This…