Balls minimize moments of logarithmic and Newtonian equilibrium measures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916166641909760 |
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| author | Clark, Carrie Laugesen, Richard S. |
| author_facet | Clark, Carrie Laugesen, Richard S. |
| contents | The $q$-th moment ($q>0$) of electrostatic equilibrium measure is shown to be minimal for a centered ball among $3$-dimensional sets of given capacity, while among $2$-dimensional sets a centered disk is the minimizer for $0<q \leq 2$. Analogous results are developed for Newtonian capacity in higher dimensions and logarithmic capacity in $2$ dimensions. Open problems are raised for Riesz equilibrium moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Balls minimize moments of logarithmic and Newtonian equilibrium measures Clark, Carrie Laugesen, Richard S. Classical Analysis and ODEs 31A15, 31B15 (Primary) 35B51 (Secondary) The $q$-th moment ($q>0$) of electrostatic equilibrium measure is shown to be minimal for a centered ball among $3$-dimensional sets of given capacity, while among $2$-dimensional sets a centered disk is the minimizer for $0<q \leq 2$. Analogous results are developed for Newtonian capacity in higher dimensions and logarithmic capacity in $2$ dimensions. Open problems are raised for Riesz equilibrium moments. |
| title | Balls minimize moments of logarithmic and Newtonian equilibrium measures |
| topic | Classical Analysis and ODEs 31A15, 31B15 (Primary) 35B51 (Secondary) |
| url | https://arxiv.org/abs/2403.12867 |