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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | 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 |
| Zitieren: | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting. Eleonora Di Nezza, Stefano Trapani and Antonio Trusiani. SIGMA 20 (2024), 039, 19 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862703643954774016 |
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| author | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| author_facet | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| citation_txt | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting. Eleonora Di Nezza, Stefano Trapani and Antonio Trusiani. SIGMA 20 (2024), 039, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-18T17:43:17Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212156 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T17:43:17Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio 2026-01-30T08:13:18Z 2024 Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting. Eleonora Di Nezza, Stefano Trapani and Antonio Trusiani. SIGMA 20 (2024), 039, 19 pages 1815-0659 2020 Mathematics Subject Classification: 32W20; 32U05; 32Q15; 35A23 arXiv:2310.10152 https://nasplib.isofts.kiev.ua/handle/123456789/212156 https://doi.org/10.3842/SIGMA.2024.039 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. The first author is supported by the project SiGMA ANR-22-ERCS-0004-02 and by the ANR-21CE40-0011 JCJC MARGE. The second author is partially supported by PRIN Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics No. 2017JZ2SW5, and by MIUR Excellence Department Projects awarded to the Department of Mathematics, University of Rome Tor Vergata, 2018–2022 CUP E83C18000100006, and 2023–2027 CUP E83C23000330006. The third author is supported by the “Knut and Alice Wallenberg Foundation”. The authors thank Chinh Lu for discussions and the anonymous referee for his comments, which helped improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting Article published earlier |
| spellingShingle | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting Di Nezza, Eleonora Trapani, Stefano Trusiani, Antonio |
| title | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting |
| title_full | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting |
| title_fullStr | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting |
| title_full_unstemmed | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting |
| title_short | Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting |
| title_sort | entropy for monge-ampère measures in the prescribed singularities setting |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212156 |
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