{"title":"唐纳森几何流的规律性","authors":"Robin S. Krom","doi":"10.1007/s40306-021-00454-x","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space <span>\\(B^{1,p}_{2}(M, {\\varLambda }^{2})\\)</span> for <i>p</i> > 4. The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson (<i>Asian J. Math.</i> <b>3</b>, 1–16 1999). For a detailed exposition see Krom and Salamon (<i>J. Symplectic Geom.</i> <b>17</b>, 381–417 2019).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00454-x.pdf","citationCount":"0","resultStr":"{\"title\":\"Regularity of the Donaldson Geometric Flow\",\"authors\":\"Robin S. Krom\",\"doi\":\"10.1007/s40306-021-00454-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space <span>\\\\(B^{1,p}_{2}(M, {\\\\varLambda }^{2})\\\\)</span> for <i>p</i> > 4. The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson (<i>Asian J. Math.</i> <b>3</b>, 1–16 1999). For a detailed exposition see Krom and Salamon (<i>J. Symplectic Geom.</i> <b>17</b>, 381–417 2019).</p></div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-10-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40306-021-00454-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Vietnamica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40306-021-00454-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-021-00454-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space \(B^{1,p}_{2}(M, {\varLambda }^{2})\) for p > 4. The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson (Asian J. Math.3, 1–16 1999). For a detailed exposition see Krom and Salamon (J. Symplectic Geom.17, 381–417 2019).
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.