3 papers
math.MG2026
Walk dimension and vanishing curve modulus in metric measure spaces
Aobo Chen
On a regular local -Dirichlet space supporting a Poincaré inequality and a capacity upper bound, we characterize the existence of curve families of positive -modulus in terms…
math.AP2025
Elliptic Harnack inequalities for mixed local and nonlocal -energy form on metric measure spaces
Aobo Chen, Zhenyu Yu
In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal -energy forms. Within this framework, we use the Poincaré inequality,…
math.MG2024
Stability of heat kernel bounds under pointed Gromov--Hausdorff convergence
Aobo Chen
We construct a conservative and strongly local regular symmetric Dirichlet form on the pointed Gromov--Hausdorff limit space and demonstrate the stability of heat kernel estimates…