4 papers
math.DG2026
Left-invariant metrics on step-two Carnot groups are uniformly doubling
Cheng Bi, Ye Zhang
We prove that the uniform doubling property holds for left-invariant Riemannian metrics on every step-two Carnot group and the sharp uniform doubling constant is , where i…
math.CA2026
Uniform volume estimates and maximal functions on generalized Heisenberg-type groups
Cheng Bi, Hong-Quan Li
On generalized Heisenberg-type groups , we give uniform volume estimates for the ball defined by a large class of Carnot-Carathéodory distan…
math.AP2024
Sharp dispersive estimates for the wave equation on the 5-dimensional lattice graph
Cheng Bi, Jiawei Cheng, Bobo Hua
Schultz \cite{S98} proved dispersive estimates for the wave equation on lattice graphs for which was extended to in \cite{BCH23}. By Newton polyhedra…
math.AP2023
The Wave Equation on Lattices and Oscillatory Integrals
Cheng Bi, Jiawei Cheng, Bobo Hua
In this paper, we establish sharp dispersive estimates for the linear wave equation on the lattice with dimension . Combining the singularity theory with result…