{"title":"On a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds","authors":"Masaya Kawamura","doi":"10.1002/mana.202300155","DOIUrl":null,"url":null,"abstract":"<p>We investigate a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds and derive a priori gradient and second-order derivative estimates for solutions to this parabolic equation. These a priori estimates give us higher order estimates and a long-time solution. Then, we can observe its behavior as <span></span><math>\n <semantics>\n <mrow>\n <mi>t</mi>\n <mo>→</mo>\n <mi>∞</mi>\n </mrow>\n <annotation>$t\\rightarrow \\infty$</annotation>\n </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4232-4272"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300155","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds and derive a priori gradient and second-order derivative estimates for solutions to this parabolic equation. These a priori estimates give us higher order estimates and a long-time solution. Then, we can observe its behavior as .
期刊介绍:
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index