The (Self-Similar, Variational) Rolling Stones
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909633470267392 |
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| author | Langharst, Dylan Ulivelli, Jacopo |
| author_facet | Langharst, Dylan Ulivelli, Jacopo |
| contents | The interplay between variational functionals and the Brunn-Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove the existence of solutions to the even logarithmic Minkowski problems arising from variational functionals, such as the first eigenvalue of the Laplacian and the torsional rigidity. In particular, we lay down a blueprint showing that the same result holds for more generic functionals by adapting the volume case from Böröczky, Lutwak, Yang, and Zhang. We show how these results imply the existence of self-similar solutions to variational flow problems à la Firey's worn stone problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02548 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The (Self-Similar, Variational) Rolling Stones Langharst, Dylan Ulivelli, Jacopo Functional Analysis Analysis of PDEs Metric Geometry 52A20, 35J05, 52A40, 49N99 The interplay between variational functionals and the Brunn-Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove the existence of solutions to the even logarithmic Minkowski problems arising from variational functionals, such as the first eigenvalue of the Laplacian and the torsional rigidity. In particular, we lay down a blueprint showing that the same result holds for more generic functionals by adapting the volume case from Böröczky, Lutwak, Yang, and Zhang. We show how these results imply the existence of self-similar solutions to variational flow problems à la Firey's worn stone problem. |
| title | The (Self-Similar, Variational) Rolling Stones |
| topic | Functional Analysis Analysis of PDEs Metric Geometry 52A20, 35J05, 52A40, 49N99 |
| url | https://arxiv.org/abs/2304.02548 |