Linlin Fan — Neckpinchhttps://neckpinch.com/authors/linlin-fan/New arXiv papers by Linlin Fan, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditionshttps://neckpinch.com/papers/2602.07989/arxiv:2602.07989Sun, 08 Feb 2026 00:00:00 GMTLinlin Fan, Peibiao Zhao — Wang, Weng and Xia[Math. Ann. 388 (2024), no. 2] studied a mean curvature type flow for the smooth, embedded capillary hypersurfaces with a constant contact angle θ∈(0,π) and confirmed the existence of solutions by the standard PDE theory. In the present paper, we study a fractional mean curvature flow for C^(1,1)-regular hypersurfaces with a capillary-type boundary condition and obtain the short time existence by the fixed point argument.Mean curvature flowVolume-preserving & constrained flowsAnisotropic & nonlocal flowsBoundaries & non-compactFree boundary & capillaryHarmonic maps & DeTurck trick