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Entropy for Monge–Ampère Measures in the Prescribed Singularities Setting
Eleonora Di Nezzaab, Stefano Trapanic, Antonio Trusianid a DMA, Ecole Normale Supérieure, Université PSL, CNRS,
45 Rue d’Ulm, 75005 Paris, France
b IMJ-PRG, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
c Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
d Chalmers University of Technology, Chalmers tvärgata 3, 41296 Göteborg, Sweden
Аннотация:
In this note, we generalize the notion of entropy for potentials in a relative full Monge–Ampère mass $\mathcal{E}(X, \theta, \phi)$, for a model potential $\phi$. 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 $\mathcal{E}^{\frac{n}{n-1}}(X, \theta, \phi)$ (provided $n>1$), while they have the same singularities of $\phi$ when $n=1$.
Ключевые слова:
Kähler manifolds, Monge–Ampère energy, entropy, big classes.
Поступила: 16 октября 2023 г.; в окончательном варианте 4 мая 2024 г.; опубликована 8 мая 2024 г.
Образец цитирования:
Eleonora Di Nezza, Stefano Trapani, Antonio Trusiani, “Entropy for Monge–Ampère Measures in the Prescribed Singularities Setting”, SIGMA, 20 (2024), 039, 19 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma2041 https://www.mathnet.ru/rus/sigma/v20/p39
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