https://neckpinch.com/authors/jiabin-yin/New arXiv papers by Jiabin Yin, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2105.09610/arxiv:2105.09610Thu, 20 May 2021 00:00:00 GMTYong Luo, Linlin Sun, Jiabin Yin — As is well known, self-similar solutions to the mean curvature flow, including self-shrinkers, translating solitons and self-expanders, arise naturally in the singularity analysis of the mean curvature flow. Recently, Guo proved that n-dimensional compact self-shrinkers in ℝⁿ⁺¹ with scalar curvature bounded from above or below by some constant are isometric to the round sphere Sⁿ(√n), which implies that n-dimensional compact self-shrinkers in ℝⁿ⁺¹ with constant scalar curvature are isometric to the round sphere Sⁿ(√n)(see also). Complete classifications of n-dimensional translating solitons in ℝⁿ⁺¹ with nonnegative constant scalar curvature and of n-dimensional self-expanders in ℝⁿ⁺¹ with nonnegative constant scalar curvature were given by Martín, Savas-Halilaj and Smoczyk and Ancari and Cheng, respectively. In this paper we give complete classifications of n-dimensional complete self-shrinkers in ℝⁿ⁺¹ with nonnegative constant scalar curvature. We will also give alternative proofs of the classification theorems due to Martín, Savas-Halilaj and Smoczyk and Ancari and Cheng.Mean curvature flowSelf-shrinkers & translatorsSingularitiesScalar curvature