A definitive majorization result for nonlinear operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916315643510784 |
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| author | Harvey, F. Reese Lawson Jr, H. Blaine |
| author_facet | Harvey, F. Reese Lawson Jr, H. Blaine |
| contents | Let ${\mathfrak g}$ be a Garding-Dirichlet operator on the set S(n) of symmetric $n\times n$ matrices. We assume that ${\mathfrak g}$ is $I$-central, that is, $D_I {\mathfrak g} = k I$ for some $k>0$. Then $$ {\mathfrak g}(A)^{1\over N} \ \geq\ {\mathfrak g}(I)^{1\over N} (\det\, A)^{1\over n} \qquad \forall\, A>0. $$ From work of Guo, Phong, Tong, Abja, Dinew, Olive and many others, this inequality has important applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A definitive majorization result for nonlinear operators Harvey, F. Reese Lawson Jr, H. Blaine Analysis of PDEs Differential Geometry 35A23, 35G20, 32Q25, 32W20, 53C55, 58J32, 35B45, 35B65 Let ${\mathfrak g}$ be a Garding-Dirichlet operator on the set S(n) of symmetric $n\times n$ matrices. We assume that ${\mathfrak g}$ is $I$-central, that is, $D_I {\mathfrak g} = k I$ for some $k>0$. Then $$ {\mathfrak g}(A)^{1\over N} \ \geq\ {\mathfrak g}(I)^{1\over N} (\det\, A)^{1\over n} \qquad \forall\, A>0. $$ From work of Guo, Phong, Tong, Abja, Dinew, Olive and many others, this inequality has important applications. |
| title | A definitive majorization result for nonlinear operators |
| topic | Analysis of PDEs Differential Geometry 35A23, 35G20, 32Q25, 32W20, 53C55, 58J32, 35B45, 35B65 |
| url | https://arxiv.org/abs/2407.05408 |