Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913344418480128 |
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| author | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| author_facet | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| contents | In this note, we generalize the notion of entropy for potentials in a relative full Monge-Ampère mass $\mathcal{E}(X, θ, ϕ)$, for a model potential $ϕ$. We then investigate stability properties of this condition with respect to blow-ups and perturbation of the cohomology class. We also prove a Moser-Trudinger type inequality with general weight and we show that functions with finite entropy lie in a relative energy class $\mathcal{E}^{\frac{n}{n-1}}(X, θ, ϕ)$ (provided $n>1$), while they have the same singularities of $ϕ$ when $n=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10152 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio Complex Variables Differential Geometry In this note, we generalize the notion of entropy for potentials in a relative full Monge-Ampère mass $\mathcal{E}(X, θ, ϕ)$, for a model potential $ϕ$. We then investigate stability properties of this condition with respect to blow-ups and perturbation of the cohomology class. We also prove a Moser-Trudinger type inequality with general weight and we show that functions with finite entropy lie in a relative energy class $\mathcal{E}^{\frac{n}{n-1}}(X, θ, ϕ)$ (provided $n>1$), while they have the same singularities of $ϕ$ when $n=1$. |
| title | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2310.10152 |