{"title":"凯勒势空间中大地线的度量下限估计","authors":"Jingchen Hu","doi":"10.1007/s12220-024-01654-1","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge–Ampère equation. As a consequence, we find that in the space of Kähler potentials any two points close to each other in <span>\\(C^2\\)</span> norm can be connected by a geodesic along which the associated metrics do not degenerate.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials\",\"authors\":\"Jingchen Hu\",\"doi\":\"10.1007/s12220-024-01654-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge–Ampère equation. As a consequence, we find that in the space of Kähler potentials any two points close to each other in <span>\\\\(C^2\\\\)</span> norm can be connected by a geodesic along which the associated metrics do not degenerate.</p>\",\"PeriodicalId\":501200,\"journal\":{\"name\":\"The Journal of Geometric Analysis\",\"volume\":\"52 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Geometric Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12220-024-01654-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01654-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials
In this paper, we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge–Ampère equation. As a consequence, we find that in the space of Kähler potentials any two points close to each other in \(C^2\) norm can be connected by a geodesic along which the associated metrics do not degenerate.
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