Work

A geometric characterization of the Maz'ya-Shaposhnikova limit on metric measure spaces

Year: 2026

Type: preprint

Abstract: We provide a purely geometric necessary and sufficient condition, in terms of a certain Cesàro mean of the volume function, for the existence of the Maz'ya-Shaposhnikova functional limit with respect to Gagliardo seminorms on metric measure spaces (under a mild measure condition). As an application, we establish the Maz'ya-Shaposhnikova convergence on the unbounded Sierpiński gasket. We also show that Ahlfors regularity does not imply the existence of this functional limit by constructing a concrete example.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.26666

Authors: Gao, Jin, Yu, Zhenyu, Zhang, Junda

Institutions: Nanjing University, National University of Defense Technology, Hangzhou Normal University, South China University of Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, National University of Defense Technology, Natural Science Foundation of Zhejiang Province

Awards: 度量测度空间上基于狄氏型和p-energy型的热核理论研究, G8439023000

OpenAlex ID: W7214099060

Cites: 1

Cited by: 1

Related to: 10