比二次曲率衰减更快的引力瞬子。我

IF 4.9 1区数学 Q1 MATHEMATICS Acta Mathematica Pub Date : 2022-01-10 DOI:10.4310/acta.2021.v227.n2.a2

Gao Chen, Xiuxiong Chen

{"title":"比二次曲率衰减更快的引力瞬子。我","authors":"Gao Chen, Xiuxiong Chen","doi":"10.4310/acta.2021.v227.n2.a2","DOIUrl":null,"url":null,"abstract":"In this paper, we study gravitational instantons (i.e., complete hyperkähler $4$‑manifolds with faster than quadratic curvature decay). We prove three main theorems: (1) Any gravitational instanton must have one of the following known ends: ALE, ALF, ALG, and ALH. (2) In the ALG and ALH non-splitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a long-standing question of Yau in the ALG and ALH cases. (3) In the ALF‑$D_k$ case, it must have an $O(4)$‑multiplet.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"4 8","pages":""},"PeriodicalIF":4.9000,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Gravitational instantons with faster than quadratic curvature decay. I\",\"authors\":\"Gao Chen, Xiuxiong Chen\",\"doi\":\"10.4310/acta.2021.v227.n2.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study gravitational instantons (i.e., complete hyperkähler $4$‑manifolds with faster than quadratic curvature decay). We prove three main theorems: (1) Any gravitational instanton must have one of the following known ends: ALE, ALF, ALG, and ALH. (2) In the ALG and ALH non-splitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a long-standing question of Yau in the ALG and ALH cases. (3) In the ALF‑$D_k$ case, it must have an $O(4)$‑multiplet.\",\"PeriodicalId\":50895,\"journal\":{\"name\":\"Acta Mathematica\",\"volume\":\"4 8\",\"pages\":\"\"},\"PeriodicalIF\":4.9000,\"publicationDate\":\"2022-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/acta.2021.v227.n2.a2\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/acta.2021.v227.n2.a2","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 7

摘要

在本文中，我们研究了引力瞬子(即，比二次曲率衰减更快的完全hyperkähler $4$ -流形)。我们证明了三个主要定理:(1)任何引力瞬子必须有以下已知端点之一:ALE, ALF, ALG和ALH。(2)在ALG和ALH非分裂情况下，它必须是生物全纯的紧复椭圆曲面减去一个除数。因此，我们在ALG和ALH病例中确认了一个长期存在的问题。(3)在ALF - $D_k$的情况下，它必须有一个$O(4)$ - multiplet。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Gravitational instantons with faster than quadratic curvature decay. I

In this paper, we study gravitational instantons (i.e., complete hyperkähler $4$‑manifolds with faster than quadratic curvature decay). We prove three main theorems: (1) Any gravitational instanton must have one of the following known ends: ALE, ALF, ALG, and ALH. (2) In the ALG and ALH non-splitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a long-standing question of Yau in the ALG and ALH cases. (3) In the ALF‑$D_k$ case, it must have an $O(4)$‑multiplet.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊