https://neckpinch.com/authors/qing-ming-cheng/New arXiv papers by Qing-Ming Cheng, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2406.11123/arxiv:2406.11123Mon, 17 Jun 2024 00:00:00 GMTQing-Ming Cheng, Junqi Lai, Guoxin Wei — In the paper, we construct, for λ>0, complete embedded and non-convex λ-hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that λ-hypersurfaces share a common conclusion on the planar domain conjecture even if the planar domain conjecture of T. Ilmanen for self-shrinkers of mean curvature flow are solved by Brendle affirmatively. Furthermore, for a fixed λ<0 which may have small |λ|, we can construct two compact embedded λ-hypersurfaces which are diffeomorphic to S¹× Sⁿ⁻¹, but they are not isometric to each other.Mean curvature flowSelf-shrinkers & translators