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math.KT2026
-ring structure in differential K-theory
Bo Liu, Xiaonan Ma
We establish the splitting principle for differential K-theory, a refinement of topological K-theory that incorporates geometric data via differential forms. Using this principle,…
math.CA2026
Dimension of Diophantine approximation and some applications in harmonic analysis
Longhui Li, Bochen Liu
In this paper we construct a new family of sets based on Diophantine approximation in the Euclidean space, and consider their applications in several problems in harmonic analysis.…
math.DG2026
Llarull's theorem on noncompact manifolds with boundary
Bo Liu, Daoqiang Liu
Recently, Zhang \cite{Zh20} and Li-Su-Wang-Zhang \cite{LSWZ24+} generalized Llarull's theorem to the noncompact complete spin manifold. In this paper, we further extend their resul…