{"title":"Erratum to “From octonions to composition superalgebras via tensor categories”","authors":"","doi":"10.4171/rmi/1469","DOIUrl":"https://doi.org/10.4171/rmi/1469","url":null,"abstract":"","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":"71 s317","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139794594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Antonio Martínez, A. Martínez-Triviño, João Paulo dos Santos
{"title":"Corrigendum to “Mean convex properly embedded $[varphi,vec{e}_{3}]$-minimal surfaces in $mathbb{R}^3$3”","authors":"Antonio Martínez, A. Martínez-Triviño, João Paulo dos Santos","doi":"10.4171/rmi/1468","DOIUrl":"https://doi.org/10.4171/rmi/1468","url":null,"abstract":"","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":"345 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140490865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper computes the spaces of extensions for the Schatten classes when they are regarded in its natural module structure over the algebra of bounded operators on the ground Hilbert space.
{"title":"Nonlinear centralizers in homology II. The Schatten classes","authors":"F. Cabello Sánchez","doi":"10.4171/rmi/1265","DOIUrl":"https://doi.org/10.4171/rmi/1265","url":null,"abstract":"The paper computes the spaces of extensions for the Schatten classes when they are regarded in its natural module structure over the algebra of bounded operators on the ground Hilbert space.","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132548017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, a rigorous proof of the orbital stability of the black soliton solution of the quintic Gross-Pitaevskii equation in one spatial dimension is obtained. We first build and show explicitly black and dark soliton solutions and we prove that the corresponding Ginzburg-Landau energy is coercive around them by using some orthogonality conditions related to perturbations of the black and dark solitons. The existence of suitable perturbations around black and dark solitons satisfying the required orthogonality conditions is deduced from an Implicit Function Theorem. In fact, these perturbations involve dark solitons with sufficiently small speeds and some proportionality factors arising from the explicit expression of their spatial derivative. We are also able to control the evolution of the modulation parameters along the quintic Gross-Pitaevskii flow by estimating their growth in time. Finally by using a low order conservation law (momentum), we prove that the speed of the perturbation is bounded and use that control to finish the proof of the orbital stability of black solitons. As a direct consequence, we also prove the orbital stability of the dark soliton in a small speed interval.
{"title":"Orbital stability of the black soliton for the quintic Gross–Pitaevskii equation","authors":"Miguel A. Alejo, A. Corcho","doi":"10.4171/rmi/1467","DOIUrl":"https://doi.org/10.4171/rmi/1467","url":null,"abstract":"In this work, a rigorous proof of the orbital stability of the black soliton solution of the quintic Gross-Pitaevskii equation in one spatial dimension is obtained. We first build and show explicitly black and dark soliton solutions and we prove that the corresponding Ginzburg-Landau energy is coercive around them by using some orthogonality conditions related to perturbations of the black and dark solitons. The existence of suitable perturbations around black and dark solitons satisfying the required orthogonality conditions is deduced from an Implicit Function Theorem. In fact, these perturbations involve dark solitons with sufficiently small speeds and some proportionality factors arising from the explicit expression of their spatial derivative. We are also able to control the evolution of the modulation parameters along the quintic Gross-Pitaevskii flow by estimating their growth in time. Finally by using a low order conservation law (momentum), we prove that the speed of the perturbation is bounded and use that control to finish the proof of the orbital stability of black solitons. As a direct consequence, we also prove the orbital stability of the dark soliton in a small speed interval.","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141221346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, loops topology, loop measures, and signatures of discrete paths. We determine the distributions of the loop homotopy class, and of the first and second homologies, defined by the lower central series of the fundamental group. This last result has yet to be extended to higher order homologies.
{"title":"On discrete loop signatures and Markov loops topology","authors":"Y. Jan","doi":"10.4171/rmi/1262","DOIUrl":"https://doi.org/10.4171/rmi/1262","url":null,"abstract":"Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, loops topology, loop measures, and signatures of discrete paths. We determine the distributions of the loop homotopy class, and of the first and second homologies, defined by the lower central series of the fundamental group. This last result has yet to be extended to higher order homologies.","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116663284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the context of a theorem of Richter, we establish a similarity between C0-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0 induced by ϕt(s)=exp(−st) for s in the right-half plane C+ acting boundedly on weighted Dirichlet spaces on C+. As a consequence, we derive a connection with the right shift semigroup {St}t≥0 given by Stf(x)={0f(x−t) if 0≤x≤t, if x>t, acting on a weighted Lebesgue space on the half line R+ and address some applications regarding the study of the invariant subspaceslinebreak of C0-semigroups of analytic 2-isometries.
{"title":"Sparse domination on non-homogeneous spaces with an application to $A_p$ weights","authors":"E. Gallardo-Gutiérrez, J. Partington","doi":"10.4171/RMI/1030","DOIUrl":"https://doi.org/10.4171/RMI/1030","url":null,"abstract":"In the context of a theorem of Richter, we establish a similarity between C0-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0 induced by ϕt(s)=exp(−st) for s in the right-half plane C+ acting boundedly on weighted Dirichlet spaces on C+. As a consequence, we derive a connection with the right shift semigroup {St}t≥0 given by \u0000Stf(x)={0f(x−t) if 0≤x≤t, if x>t, \u0000acting on a weighted Lebesgue space on the half line R+ and address some applications regarding the study of the invariant subspaceslinebreak of C0-semigroups of analytic 2-isometries.","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129958370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Local monomialization of a system of first integrals of Darboux type","authors":"André Belotto da Silva","doi":"10.4171/rmi/1012","DOIUrl":"https://doi.org/10.4171/rmi/1012","url":null,"abstract":"","PeriodicalId":239929,"journal":{"name":"Revista Matemática Iberoamericana","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122338142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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