https://neckpinch.com/authors/yuntao-zhang/New arXiv papers by Yuntao Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2412.18102/arxiv:2412.18102Tue, 24 Dec 2024 00:00:00 GMTLaiyuan Gao, Shicheng Zhang, Yuntao Zhang — Mayer asks a question what closed, embedded and nonconvex initial curves guarantee that Gage's area-preserving flow (GAPF) exists globally. A folklore conjecture since 2012 says that GAPF evolves smooth, embedded and star-shaped initial curves globally. In this paper, we prove this conjecture by using Dittberner's singularity analysis theory. A star-shaped "flying wing" curve is constructed to show that GAPF may not always preserve the star-shapedness of evolving curves. This example is also a negative answer to Mantegazza's open problem whether the curve shortening flow (CSF) always preserves the star shape of the evolving curves.Curve shorteningVolume-preserving & constrained flowsSingularities