https://neckpinch.com/authors/hsiao-fan-liu/New arXiv papers by Hsiao-Fan Liu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1801.10347/arxiv:1801.10347Wed, 31 Jan 2018 00:00:00 GMTHsiao-Fan Liu — The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is integrable if the local differential invariants of a solution to the curve flow evolve according to a soliton equation. In this paper, we show that this flow on S³ and ℍ³ are integrable, and describe algebraically explicit solutions to such curve flows. The Cauchy problem of the curve flows on S³ and ℍ³ and its Bäcklund transformations follow from this construction.Mean curvature flow3-manifolds