https://neckpinch.com/authors/xiaoqian-xin/New arXiv papers by Xiaoqian Xin, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.08283/arxiv:2610.08283Tue, 06 Oct 2026 00:00:00 GMTTianhong Pu, Xiaoqian Xin, Lixia Yuan — We study a positive radial graph evolving by V=H^α+b, with α>0 and b<0, in the unit cylinder and with uᵣ(1,t)=u(1,t). We separate finite-time continuation estimates from the time-uniform interior estimates needed for convergence of normalized translates. On existing classical intervals we prove height and gradient bounds and an explicit conversion of velocity bounds into estimates for H, uᵣ/r, and uᵣᵣ. We derive the correct boundary defect for comparisons with finite-slope translators. Under independent interior velocity bounds and two-sided slope trapping, we prove compactness and identify every translated limit with the cup translator. We identify the radial zero-number comparison still required to establish that trapping. Stationary caps and power-law Robin laws are included.Mean curvature flowSelf-shrinkers & translatorsSingularitiesLimit spaces & RCDBoundaries & non-compact https://neckpinch.com/papers/2610.08270/arxiv:2610.08270Tue, 06 Oct 2026 00:00:00 GMTTianhong Pu, Xiaoqian Xin, Lixia Yuan, Xiaoyu Zhang — We study the graphical forced mean curvature flow in a planar strip subject to Robin boundary conditions. The normal velocity is prescribed by V=H+b, where b>0 is constant and H denotes the curvature of the graph. We consider positive even solutions and reduce the problem to the half interval. The main results describe the degeneration produced by the Robin condition: the height, the instantaneous velocity, and the spatial gradient diverge, while the normalized slope uₓ/u converges to one away from the symmetry axis. The normalized velocity uₜ/u converges to the forcing parameter b. The curvature converges to zero in the interior in an integral sense, whereas its horizontal curvature measure concentrates at the symmetry axis.Mean curvature flowOther curvature flowsVolume-preserving & constrained flowsBoundaries & non-compact