https://neckpinch.com/authors/daniel-tataru/New arXiv papers by Daniel Tataru, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2512.21634arxiv:2512.21634Thu, 25 Dec 2025 00:00:00 GMTJiaxi Huang, Daniel Tataru — The skew mean curvature flow is an evolution equation for d dimensional ma\-nifolds embedded in ℝ^(d+2) (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove large data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 2. This is achieved by introducing several new ideas: (i) a time discretization method to establish the existence of smooth solutions, (ii) constructing the orthonormal frame by a parallel transport method and a lifting criterion, (iii) introducing intrinsic fractional function spaces X^s⊂ H^s on a noncompact manifold for any s>d/2, such that the X^s-norm of the second fundamental form can be propagated well along the quasilinear Schrödinger flow, (iv) deriving a difference equation to prove the uniqueness result for solutions F∈ C², which is independent in the choices of gauge. Our method turns out to be more robust for large data problem.Mean curvature flowStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2209.08941arxiv:2209.08941Mon, 19 Sep 2022 00:00:00 GMTJiaxi Huang, Ze Li, Daniel Tataru — The skew mean curvature flow is an evolution equation for a d dimensional manifold immersed into 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≥ 4. This extends the local well-posedness result in.Mean curvature flow https://arxiv.org/abs/2202.10632arxiv:2202.10632Tue, 22 Feb 2022 00:00:00 GMTJiaxi Huang, Daniel Tataru — The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in ℝ^(d+2) (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In an earlier paper, the authors introduced a harmonic/Coulomb gauge formulation of the problem, and used it to prove small data local well-posedness in dimensions d ≥ 4. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 2. This is achieved by introducing a new, heat gauge formulation of the equations, which turns out to be more robust in low dimensions.Mean curvature flow