Fractal curvatures and short-time asymptotics of heat content
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915448415584256 |
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| author | Rozanova-Pierrat, Anna Teplyaev, Alexander Winter, Steffen Zähle, Martina |
| author_facet | Rozanova-Pierrat, Anna Teplyaev, Alexander Winter, Steffen Zähle, Martina |
| contents | The aim of our paper is twofold. First, we present new mathematical developments on the analysis of de Gennes' hypothesis on the short-time asymptotics of the heat content for bounded domains with smooth boundary and with fractal boundary. Second, we discuss new findings and concepts related to fractal curvatures for domains with fractal boundary. We conjecture that fractal curvatures and their scaling exponents will emerge in the short-time heat content asymptotics of domains with fractal boundary and the results discussed here are small initial contributions towards a resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractal curvatures and short-time asymptotics of heat content Rozanova-Pierrat, Anna Teplyaev, Alexander Winter, Steffen Zähle, Martina Analysis of PDEs Mathematical Physics Differential Geometry Functional Analysis The aim of our paper is twofold. First, we present new mathematical developments on the analysis of de Gennes' hypothesis on the short-time asymptotics of the heat content for bounded domains with smooth boundary and with fractal boundary. Second, we discuss new findings and concepts related to fractal curvatures for domains with fractal boundary. We conjecture that fractal curvatures and their scaling exponents will emerge in the short-time heat content asymptotics of domains with fractal boundary and the results discussed here are small initial contributions towards a resolution. |
| title | Fractal curvatures and short-time asymptotics of heat content |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2502.02989 |