{"title":"紧凑超卡勒流形上的完全非线性椭圆方程","authors":"Giovanni Gentili, Luigi Vezzoni","doi":"arxiv-2409.00420","DOIUrl":null,"url":null,"abstract":"We consider a general class of elliptic equations on hypercomplex manifolds\nwhich includes the quaternionic Monge-Amp\\`ere equation, the quaternionic\nHessian equation and the Monge-Amp\\`ere equation for quaternionic\n$(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions\nthe solutions to these equations on hyperk\\\"ahler manifolds satisfy a\n$C^{2,\\alpha}$ a priori estimate.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fully non-linear elliptic equations on compact hyperkähler manifolds\",\"authors\":\"Giovanni Gentili, Luigi Vezzoni\",\"doi\":\"arxiv-2409.00420\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a general class of elliptic equations on hypercomplex manifolds\\nwhich includes the quaternionic Monge-Amp\\\\`ere equation, the quaternionic\\nHessian equation and the Monge-Amp\\\\`ere equation for quaternionic\\n$(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions\\nthe solutions to these equations on hyperk\\\\\\\"ahler manifolds satisfy a\\n$C^{2,\\\\alpha}$ a priori estimate.\",\"PeriodicalId\":501113,\"journal\":{\"name\":\"arXiv - MATH - Differential Geometry\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.00420\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.00420","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fully non-linear elliptic equations on compact hyperkähler manifolds
We consider a general class of elliptic equations on hypercomplex manifolds
which includes the quaternionic Monge-Amp\`ere equation, the quaternionic
Hessian equation and the Monge-Amp\`ere equation for quaternionic
$(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions
the solutions to these equations on hyperk\"ahler manifolds satisfy a
$C^{2,\alpha}$ a priori estimate.
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