{"title":"Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem","authors":"James Eldred Pascoe","doi":"10.2748/tmj.20220412","DOIUrl":"https://doi.org/10.2748/tmj.20220412","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1232 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139019019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Erratum by editorial office: Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential (Tohoku Math.J. 75 (2023), 215--232)","authors":"Naoki Matsui","doi":"10.2748/tmj.20231115","DOIUrl":"https://doi.org/10.2748/tmj.20231115","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"349 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139018370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Weighted $L^2$ harmonic 1-forms and the topology at infinity of complete noncompact weighted manifolds","authors":"Keomkyo Seo, Gabjin Yun","doi":"10.2748/tmj.20220513","DOIUrl":"https://doi.org/10.2748/tmj.20220513","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"87 10","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139017399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the Euler-Lagrange system associated with the extremal sequences of the discrete Hardy-Littlewood-Sobolev inequality with the Sobolev-type critical conditions. This system comes into play in estimating bounds of the Coulomb energy and is related to the study of conformal geometry. In discrete case, we show that if the solutions of the system are summable, they must be monotonically decreasing at infinity. Moreover, the decay rates of the solutions are obtained. By estimating the infinite series, we prove that the Serrin-type condition is critical for the existence of super-solutions of the system. In addition, we also obtain analogous properties of the Euler-Lagrange system of the extremal sequences of the discrete reversed Hardy-Littlewood-Sobolev inequality.
{"title":"Critical conditions and asymptotics for discrete systems of the Hardy-Littlewood-Sobolev type","authors":"Yutian Lei, Yayun Li, Ting Tang","doi":"10.2748/tmj.20220107","DOIUrl":"https://doi.org/10.2748/tmj.20220107","url":null,"abstract":"In this paper, we study the Euler-Lagrange system associated with the extremal sequences of the discrete Hardy-Littlewood-Sobolev inequality with the Sobolev-type critical conditions. This system comes into play in estimating bounds of the Coulomb energy and is related to the study of conformal geometry. In discrete case, we show that if the solutions of the system are summable, they must be monotonically decreasing at infinity. Moreover, the decay rates of the solutions are obtained. By estimating the infinite series, we prove that the Serrin-type condition is critical for the existence of super-solutions of the system. In addition, we also obtain analogous properties of the Euler-Lagrange system of the extremal sequences of the discrete reversed Hardy-Littlewood-Sobolev inequality.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134962154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We define a notion of adelic Euler systems for $mathbb{G}_m$ over arbitrary number fields and prove that all such systems over $mathbb{Q}$ are cyclotomic in nature. We deduce that all Euler systems for $mathbb{G}_m$ over $mathbb{Q}$ are cyclotomic, as has been conjectured by Coleman, if and only if they validate an analogue of Leopoldt's Conjecture.
{"title":"Adelic Euler systems for $mathbb{G}_m$","authors":"David Burns, Alexandre Daoud","doi":"10.2748/tmj.20220111","DOIUrl":"https://doi.org/10.2748/tmj.20220111","url":null,"abstract":"We define a notion of adelic Euler systems for $mathbb{G}_m$ over arbitrary number fields and prove that all such systems over $mathbb{Q}$ are cyclotomic in nature. We deduce that all Euler systems for $mathbb{G}_m$ over $mathbb{Q}$ are cyclotomic, as has been conjectured by Coleman, if and only if they validate an analogue of Leopoldt's Conjecture.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134962234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $mathscr{H}^{n}(1)$, of center at origin and radius 1, in the $(n+1)$-dimensional Lorentz-Minkowski space $mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $mathscr{H}^{n}(1)$, as time tends to infinity. Clearly, this conclusion is an extension of our previous work [2].
{"title":"An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${mathbb R}^{n+1}_1$","authors":"Ya Gao, Jing Mao","doi":"10.2748/tmj.20220203","DOIUrl":"https://doi.org/10.2748/tmj.20220203","url":null,"abstract":"In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $mathscr{H}^{n}(1)$, of center at origin and radius 1, in the $(n+1)$-dimensional Lorentz-Minkowski space $mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $mathscr{H}^{n}(1)$, as time tends to infinity. Clearly, this conclusion is an extension of our previous work [2].","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134962224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose a method to study plane curves deformations in the Minkowski plane taking into consideration their geometry as well as their singularities. This method is an extension of the method proposed by Salarinoghabi and Tari to curves in the Euclidean plane. We deal in detail with all local phenomena that occur generically in 2-parameters families of curves. In each case, we obtain the geometry of the deformed curve, that is, information about inflections, vertices and lightlike points. We also obtain the behavior of the evolute/caustic of a curve at especial points and the bifurcations that can occur when the curve is deformed.
{"title":"Geometric deformations of curves in the Minkowski plane","authors":"Alex Paulo Francisco","doi":"10.2748/tmj.20220221","DOIUrl":"https://doi.org/10.2748/tmj.20220221","url":null,"abstract":"In this paper, we propose a method to study plane curves deformations in the Minkowski plane taking into consideration their geometry as well as their singularities. This method is an extension of the method proposed by Salarinoghabi and Tari to curves in the Euclidean plane. We deal in detail with all local phenomena that occur generically in 2-parameters families of curves. In each case, we obtain the geometry of the deformed curve, that is, information about inflections, vertices and lightlike points. We also obtain the behavior of the evolute/caustic of a curve at especial points and the bifurcations that can occur when the curve is deformed.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134962157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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