Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Di Nezza, Eleonora, Trapani, Stefano, Trusiani, Antonio
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212156
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting. Eleonora Di Nezza, Stefano Trapani and Antonio Trusiani. SIGMA 20 (2024), 039, 19 pages

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...