Conghan Dong

Journal Article Inventiones Mathematicae · January 1, 2025 We show that the Euclidean 3-space R3 is stable for the Positive Mass Theorem in the following sense. Let (Mi,gi) be a sequence of complete asymptotically flat 3-manifolds with nonnegative scalar curvature and suppose that the ADM mass m(gi) of one end of ... Full text Cite

Volume Gap Theorems for Ricci Nonnegative Metrics and Einstein Metrics

Journal Article Journal of Mathematical Study · January 1, 2025 In this note, we prove some gap theorems of asymptotic volume ratio for Ricci nonnegative metrics, and gap theorems of volume for Einstein metrics. ... Full text Cite

Some stability results of positive mass theorem for uniformly asymptotically flat 3-manifolds

Journal Article Annales Mathematiques Du Quebec · October 1, 2024 In this paper, we show that for a sequence of orientable complete uniformly asymptotically flat 3-manifolds (Mi,gi) with nonnegative scalar curvature and ADM mass m(gi) tending to zero, by subtracting some open subsets Z Full text Cite

Three-Manifolds with Bounded Curvature and Uniformly Positive Scalar Curvature

Journal Article Journal of Geometric Analysis · June 1, 2023 In this note, we prove that for a complete noncompact three-dimensional Riemannian manifold with bounded sectional curvature, if it has uniformly positive scalar curvature, then there is a uniform lower bound on the injectivity radius. ... Full text Cite

W 1, p -metrics and conformal metrics with L n/2-bounded scalar curvature

Journal Article Communications in Contemporary Mathematics · February 1, 2023 A W1,p-metric on an n-dimensional closed Riemannian manifold naturally induces a distance function, provided p is sufficiently close to n. If a sequence of metrics gk converges in W1,p to a limit metric g, then the corresponding distance functio ... Full text Cite

Compactness of Conformal Metrics with Integral Bounds on Ricci Curvature

Journal Article Pacific Journal of Mathematics · January 1, 2022 Let (M, g) be a closed Riemannian manifold with dimension n > 2, and (Equation Presented) be a noncollapsing conformal metric sequence with fixed volume. We prove that { loguk is compact in C0,αif ∥Ric(gk)∥LP(M,g ... Full text Cite