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Intrinsic Flat Convergence of Points and Applications to Stability of the Positive Mass Theorem

https://doi.org/10.1007/s00023-022-01158-0

Huang, Lan-Hsuan ; Lee, Dan A. ; Perales, Raquel ( July 2022 , Annales Henri Poincaré)

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Alexandrov spaces with integral current structure

https://doi.org/https://dx.doi.org/10.4310/CAG.2021.v29.n1.a4

Jaramillo, Maree ; Perales, Raquel ; Rajan, Priyanka ; Searle, Catherine ; Siffert, Anna ( January 2021 , 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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Maximal volume entropy rigidity for RCD∗(−(N − 1),N) spaces

https://doi.org/http://doi.org/10.1112/jlms.12470

Connell, Chris ; Dai, Xianzhe ; N´u˜nez-Zimbr´on, Jes´us ; Perales, Raquel ; Su´arez-Serrato, Pablo ; Wei, Guofang ( June 2021 , Journal of the London Mathematical Society)
null (Ed.)
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