{"title":"存在里曼度量时最小曲面方程的逆问题","authors":"Janne Nurminen","doi":"10.1088/1361-6544/ad6949","DOIUrl":null,"url":null,"abstract":"In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold where the metric is of the form . Here is a simple Riemannian metric on , e is the Euclidean metric on and c a smooth positive function. We show that if the associated Dirichlet-to-Neumann maps corresponding to metrics g and agree, then the Taylor series of the conformal factor at is equal to a positive constant. We also show a partial data result when n = 3.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"27 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An inverse problem for the minimal surface equation in the presence of a riemannian metric\",\"authors\":\"Janne Nurminen\",\"doi\":\"10.1088/1361-6544/ad6949\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold where the metric is of the form . Here is a simple Riemannian metric on , e is the Euclidean metric on and c a smooth positive function. We show that if the associated Dirichlet-to-Neumann maps corresponding to metrics g and agree, then the Taylor series of the conformal factor at is equal to a positive constant. We also show a partial data result when n = 3.\",\"PeriodicalId\":54715,\"journal\":{\"name\":\"Nonlinearity\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinearity\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6544/ad6949\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad6949","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
在这项工作中，我们研究了黎曼流形上最小曲面方程的逆问题，其中的度量形式为 。这里是一个简单的黎曼流形，e 是欧几里得流形，c 是一个光滑的正函数。我们证明，如果对应于度量 g 的相关迪里希勒到诺伊曼映射一致，那么保角因子 at 的泰勒级数等于一个正常数。我们还展示了 n = 3 时的部分数据结果。
An inverse problem for the minimal surface equation in the presence of a riemannian metric
In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold where the metric is of the form . Here is a simple Riemannian metric on , e is the Euclidean metric on and c a smooth positive function. We show that if the associated Dirichlet-to-Neumann maps corresponding to metrics g and agree, then the Taylor series of the conformal factor at is equal to a positive constant. We also show a partial data result when n = 3.
期刊介绍：
Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest.
Subject coverage:
The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal.
Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena.
Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
