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math.CA2022
A Rademacher type theorem for Hamiltonians and application to absolute minimizers
Jiayin Liu, Yuan Zhou
We establish a Rademacher type theorem involving Hamiltonians under very weak conditions in both of Euclidean and Carnot-Carathéodory spaces. In particular, is ass…
math.CA2021★ 4 cited
On the Dimension of Kakeya Sets in the First Heisenberg Group
Jiayin Liu
We define Kakeya sets in the Heisenberg group and show that the Heisenberg Hausdorff dimension of Kakeya sets in the first Heisenberg group is at least 3. This lower bound is sharp…