{"title":"(ℂ-)凸域挤压函数的显式通用边界","authors":"Gautam Bharali, Nikolai Nikolov","doi":"10.1142/s0129167x24500319","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we prove two separate lower bounds — one for nondegenerate convex domains and the other for nondegenerate <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℂ</mi></math></span><span></span>-convex (but not necessarily convex) domains — for the squeezing function that hold true for all domains in <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>, for a fixed <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, of the stated class. We provide explicit expressions in terms of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span> for these estimates.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"72 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Explicit universal bounds for squeezing functions of (ℂ-)convex domains\",\"authors\":\"Gautam Bharali, Nikolai Nikolov\",\"doi\":\"10.1142/s0129167x24500319\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we prove two separate lower bounds — one for nondegenerate convex domains and the other for nondegenerate <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>ℂ</mi></math></span><span></span>-convex (but not necessarily convex) domains — for the squeezing function that hold true for all domains in <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>, for a fixed <span><math altimg=\\\"eq-00004.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>n</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, of the stated class. We provide explicit expressions in terms of <span><math altimg=\\\"eq-00005.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>n</mi></math></span><span></span> for these estimates.</p>\",\"PeriodicalId\":54951,\"journal\":{\"name\":\"International Journal of Mathematics\",\"volume\":\"72 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0129167x24500319\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0129167x24500319","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们为挤压函数证明了两个独立的下界--一个是非退化凸域的下界,另一个是非退化ℂ-凸域(但不一定是凸)的下界,这两个下界对于所述类别中固定 n≥2 的ℂn 中的所有域都成立。我们为这些估计值提供了以 n 为单位的明确表达式。
Explicit universal bounds for squeezing functions of (ℂ-)convex domains
In this paper, we prove two separate lower bounds — one for nondegenerate convex domains and the other for nondegenerate -convex (but not necessarily convex) domains — for the squeezing function that hold true for all domains in , for a fixed , of the stated class. We provide explicit expressions in terms of for these estimates.
期刊介绍:
The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.