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  1. ; ; ; ; ( , Communications in analysis and geometry)
    Liu, Kefeng (Ed.)
    We endow each closed, orientable Alexandrov space (X, d) with an integral current T of weight equal to 1, ∂T = 0 and set(T) = X, in other words, we prove that (X, d, T) is an integral current space with no boundary. Combining this result with a result of Li and Perales, we show that non-collapsing sequences of these spaces with uniform lower curvature and diameter bounds admit subsequences whose Gromov-Hausdorff and intrinsic flat limits agree. 
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  2. ; ( , Proceedings of the American Mathematical Society)
    Wei, Guofang (Ed.)
    We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank, giving a classification of closed, smooth, simply-connected 4-manifolds of almost non-negative curvature under the assumption of torus symmetry. 
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