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math.MG2025
On the Structure of Busemann Spaces with Non-Negative Curvature I
Bang-Xian Han, Liming Yin
We extend the structure theory of Burago--Gromov--Perelman for Alexandrov spaces with curvature bounded below, to the setting of Busemann spaces with non-negative curvature. We pro…
math.FA2025
A new characterization of Sobolev spaces on Lipschitz differentiability spaces
Bang-Xian Han, Zhe-Feng Xu, Zhuo-Nan Zhu
Numerous characterizations of Sobolev norms via the asymptotic behavior of non-local functionals have been established over the past decades; however, their validity beyond the PI…
math.MG2025
Barycenter curvature-dimension condition for extended metric measure spaces
Bang-Xian Han, Deng-yu Liu, Zhuo-nan Zhu
In this survey, we introduce a new curvature-dimension condition for extended metric measure spaces, called Barycenter-Curvature Dimension condition BCD, from the perspective of Wa…