Large dimension behavior of the Hessian eigenvalues of the unit balls
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916958640799744 |
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| author | Le, Nam Q. |
| author_facet | Le, Nam Q. |
| contents | We show that a sequence of $k$-Hessian eigenvalues of the unit ball in ${\mathbb R}^n$ stays bounded as long as the ratio $n/k$ stays bounded. Moreover, we identify their growth of order at least $(2-1/k)$ in $n/k$. In the case $k=n$, we show that the Monge--Ampère eigenvalues of the unit balls tend to $4$ in the large dimension limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large dimension behavior of the Hessian eigenvalues of the unit balls Le, Nam Q. Analysis of PDEs We show that a sequence of $k$-Hessian eigenvalues of the unit ball in ${\mathbb R}^n$ stays bounded as long as the ratio $n/k$ stays bounded. Moreover, we identify their growth of order at least $(2-1/k)$ in $n/k$. In the case $k=n$, we show that the Monge--Ampère eigenvalues of the unit balls tend to $4$ in the large dimension limit. |
| title | Large dimension behavior of the Hessian eigenvalues of the unit balls |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.09409 |