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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…
math.FA2024
Besov-Lipschitz norm and -energy measure on scale-irregular Vicsek sets
Aobo Chen, Jin Gao, Zhenyu Yu +1
In this paper, we establish the existence of -energy norms and the corresponding -energy measures for scale-irregular Vicsek sets, which may lack self-similarity. We also inv…
math.PR2024
Boundary Harnack principle on uniform domains
Aobo Chen
We present a proof of scale-invariant boundary Harnack principle for uniform domains when the underlying space satisfies a scale-invariant elliptic Harnack inequality. Our approach…