A remark on a conjecture on the symmetric Gaussian Problem
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913357291847680 |
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| author | Fusco, Nicola La Manna, Domenico Angelo |
| author_facet | Fusco, Nicola La Manna, Domenico Angelo |
| contents | In this paper we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centered at the origin is the only minimizer of such a functional for certain value of the mass. We give a positive answer in dimension two while in higher dimension the situation is different. In fact, for small value of mass the ball centered at the origin is a local minimizer while for large values the ball is a maximizer among convex sets with uniform bound on the curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04522 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A remark on a conjecture on the symmetric Gaussian Problem Fusco, Nicola La Manna, Domenico Angelo Analysis of PDEs In this paper we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centered at the origin is the only minimizer of such a functional for certain value of the mass. We give a positive answer in dimension two while in higher dimension the situation is different. In fact, for small value of mass the ball centered at the origin is a local minimizer while for large values the ball is a maximizer among convex sets with uniform bound on the curvature. |
| title | A remark on a conjecture on the symmetric Gaussian Problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2306.04522 |