https://neckpinch.com/authors/yueheng-bao/New arXiv papers by Yueheng Bao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.09557arxiv:2610.09557Wed, 07 Oct 2026 00:00:00 GMTYueheng Bao, Lorenzo Sarnataro — We provide an alternative and independent proof of the analogue of the Gage-Hamilton-Grayson Theorem for embedded free boundary curve shortening flows in a convex planar domain established by Langford-Zhu. Our proof is based on blowup arguments introduced by B. White in his work on mean-convex mean curvature flow.Mean curvature flowCurve shorteningSingularitiesFree boundary & capillary https://arxiv.org/abs/2609.01026arxiv:2609.01026Tue, 01 Sep 2026 00:00:00 GMTYueheng Bao, Robert Haslhofer — In this article, we introduce a new distance function between hypersurfaces with free boundary. We show that our new quantity, which we call twisted Fermi distance, is monotone under mean curvature flow with free boundary. This overcomes the stumbling block that monotonicity of the usual distance function can fail for non-convex domains, and has several applications. Most importantly, we generalize the avoidance principle for free boundary Brakke flows, recently established by the first author for convex domains, to arbitrary domains. Using this, we then show that all results from our recent joint work, including the mean-convex neighborhood theorem and the uniqueness theorem for free boundary flows through cylindrical singularities, can be generalized to arbitrary domains without any convexity assumptions as well.Mean curvature flowSingularitiesWeak & singular flowsStability & uniquenessFree boundary & capillary https://arxiv.org/abs/2606.17353arxiv:2606.17353Mon, 15 Jun 2026 00:00:00 GMTYueheng Bao, Robert Haslhofer — We consider mean curvature flow with free boundary through cylindrical or half-cylindrical singularities, namely singularities of the types ℝ^k× S^(n-k), ℝ^k_+× S^(n-k) or ℝ^k× S^(n-k)_+. Using the foundational results for free boundary Brakke flows by Edelen and the first author, and the recent classification of ancient asymptotically cylindrical flows by Bamler-Lai, we prove that all these singularities have a mean-convex neighborhood. Moreover, generalizing work of Hershkovits-White to the free boundary setting we show that the free boundary level set flow is nonfattening provided all singularities have a mean-convex neighborhood. We conclude that free boundary flow through singularities is well-posed as long as all singularities are of cylindrical or half-cylindrical type.Mean curvature flowAncient solutionsSingularitiesWeak & singular flowsFree boundary & capillary