On the dichotomy of $p$-walk dimensions on metric measure spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915634292457472 |
|---|---|
| author | Yang, Meng |
| author_facet | Yang, Meng |
| contents | On a volume doubling metric measure space endowed with a family of $p$-energies such that the Poincaré inequality and the cutoff Sobolev inequality with $p$-walk dimension $β_p$ hold, for $p$ in an open interval $I\subseteq (1,+\infty)$, we prove the following dichotomy: either $β_p=p$ for all $p\in I$, or $β_p>p$ for all $p\in I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the dichotomy of $p$-walk dimensions on metric measure spaces Yang, Meng Functional Analysis Analysis of PDEs Metric Geometry 31E05, 28A80 On a volume doubling metric measure space endowed with a family of $p$-energies such that the Poincaré inequality and the cutoff Sobolev inequality with $p$-walk dimension $β_p$ hold, for $p$ in an open interval $I\subseteq (1,+\infty)$, we prove the following dichotomy: either $β_p=p$ for all $p\in I$, or $β_p>p$ for all $p\in I$. |
| title | On the dichotomy of $p$-walk dimensions on metric measure spaces |
| topic | Functional Analysis Analysis of PDEs Metric Geometry 31E05, 28A80 |
| url | https://arxiv.org/abs/2509.08641 |