Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting
In this note, we generalize the notion of entropy for potentials in a relatively full Monge-Ampère mass ℰ(, , ), for a model potential . 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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212156 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting. Eleonora Di Nezza, Stefano Trapani and Antonio Trusiani. SIGMA 20 (2024), 039, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | In this note, we generalize the notion of entropy for potentials in a relatively full Monge-Ampère mass ℰ(, , ), for a model potential . 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 ℰ↑(/(−1))(, , ) (provided > 1), while they have the same singularities of when = 1.
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| ISSN: | 1815-0659 |