Add to ORKGThe skew mean curvature flow is an evolution equation for a $d$ dimensional manifold immersed into $\mathbb{R}^{d+2}$, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature flow in dimensions $d\geq 4$. This extends the local well-posedness result in \cite{HT}.Comment: 38 page
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We study local regularity and singularity for the evolution of m-harmonic maps on ℝ[m] into a smooth...
We prove the longtime existence for mean curvature flow of a smooth n-dimensional spacelike submani...
In this thesis, we present two results from fields situated at two different extremities of the broa...
The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (...
The skew mean curvature flow is an evolution equation for $d$ dimensional manifolds embedded in $\ma...
We construct smooth mean curvature flows with surgery that approximate weak mean curvature flows wit...
We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ avoids asymptoti...
In this work, we construct distance like functions with integral hessian bound on manifolds with sma...
This dissertation concerns the mean curvature flow, a geometric evolution equation for submanifolds,...
In this paper, we show the existence and uniqueness of short-time very regular or smooth solution to...
We prove higher regularity properties of inverse mean curvature flow in Euclidean space: A sharp low...
We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds,...
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric ...
For an $H>0$ rotationally symmetric embedded torus $N_{0} \subset \mathbb{R}^{3}$, evolved by Invers...
We establish geometric regularity for Type I blow-up limits of the K\"ahler-Ricci flow based at any ...
We study local regularity and singularity for the evolution of m-harmonic maps on ℝ[m] into a smooth...
We prove the longtime existence for mean curvature flow of a smooth n-dimensional spacelike submani...
In this thesis, we present two results from fields situated at two different extremities of the broa...