https://neckpinch.com/authors/conghan-dong/New arXiv papers by Conghan Dong, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2607.20741arxiv:2607.20741Wed, 22 Jul 2026 00:00:00 GMTConghan Dong — Let (M³, g, k) be a smooth, connected, asymptotically flat initial data set with connected outermost past apparent horizon Σ. We prove the Penrose conjecture, namely that m_ADM(g) ≥ √(|Σ|)/(16 π), under the assumptions of the dominant energy condition and the 2-convexity condition that the sum of the two smallest eigenvalues of k is nonnegative. The main tool is the σ-inverse mean curvature flow, together with a monotonicity formula developed in.Mean curvature flowOther curvature flowsInverse mean curvature flowBoundaries & non-compactEigenvalues & spectrumPhysics https://arxiv.org/abs/2605.26504arxiv:2605.26504Tue, 26 May 2026 00:00:00 GMTConghan Dong — Let (M³, g, k) be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let m denote its ADM mass. The generalized Penrose conjecture asserts that the area of an outermost generalized apparent horizon N⊂ M satisfies |N| ≤ 16 πm². In this paper, we establish this inequality for each connected component of N in the case where k is proportional to the metric g. Our approach is based on a new geometric evolution, which we call the σ-inverse mean curvature flow, together with a novel monotonicity formula that may be of independent interest.Mean curvature flowOther curvature flowsInverse mean curvature flowBoundaries & non-compactPhysics https://arxiv.org/abs/2412.13546arxiv:2412.13546Wed, 18 Dec 2024 00:00:00 GMTConghan Dong, Yu Li — We establish a uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and a uniform curvature bound. Additionally, we extend the non-collapsing result to a broader class of smooth metric measure spaces satisfying Bakry-Émery conditions.Ricci solitons(Non)collapsingLimit spaces & RCD