We prove the strong-type and weak-type estimates for the Calderon–Zygmund singular integrals on central Morrey–Orlicz and weak central Morrey–Orlicz spaces defined in our earlier paper [26]. Next ...
{"title":"Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces","authors":"L. Maligranda, Katsuo Matsuoka","doi":"10.2748/tmj/1593136820","DOIUrl":"https://doi.org/10.2748/tmj/1593136820","url":null,"abstract":"We prove the strong-type and weak-type estimates for the Calderon–Zygmund singular integrals on central Morrey–Orlicz and weak central Morrey–Orlicz spaces defined in our earlier paper [26]. Next ...","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45511428","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}
Based on the idea of adiabatic expansion theory, we will present a new formula for the asymptotic expansion coefficients of every derivative of the heat kernel on a compact Riemannian manifold. It will be very useful for having systematic understanding of the coefficients, and, furthermore, by using only a basic knowledge of calculus added to the formula, one can describe them explicitly up to an arbitrarily high order.
{"title":"A formula for the heat kernel coefficients on Riemannian manifolds","authors":"M. Nagase","doi":"10.2748/tmj/1593136821","DOIUrl":"https://doi.org/10.2748/tmj/1593136821","url":null,"abstract":"Based on the idea of adiabatic expansion theory, we will present a new formula for the asymptotic expansion coefficients of every derivative of the heat kernel on a compact Riemannian manifold. It will be very useful for having systematic understanding of the coefficients, and, furthermore, by using only a basic knowledge of calculus added to the formula, one can describe them explicitly up to an arbitrarily high order.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"72 1","pages":"261-282"},"PeriodicalIF":0.5,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43156169","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 prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of "goodness". In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we give details on the classical results needed for the proofs.
{"title":"Quadratic relations between periods of connections","authors":"J. Fres'an, C. Sabbah, Jeng-Daw Yu","doi":"10.2748/tmj.20211209","DOIUrl":"https://doi.org/10.2748/tmj.20211209","url":null,"abstract":"We prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of \"goodness\". In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we give details on the classical results needed for the proofs.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42432945","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}
Conformally Kahler, Einstein-Maxwell metrics and $f$-extremal metrics are generalization of canonical metrics in Kahler geometry. We introduce uniform K-stability for toric Kahler manifolds, and show that uniform K-stability is necessary condition for the existence of $f$-extremal metrics on toric manifolds. Furthermore, we show that uniform K-stability is equivalent to properness of relative K-energy.
{"title":"Uniform K-stability and Conformally Kähler, Einstein-Maxwell geometry on toric manifolds","authors":"Yaxiong Liu","doi":"10.2748/tmj.20201006","DOIUrl":"https://doi.org/10.2748/tmj.20201006","url":null,"abstract":"Conformally Kahler, Einstein-Maxwell metrics and $f$-extremal metrics are generalization of canonical metrics in Kahler geometry. We introduce uniform K-stability for toric Kahler manifolds, and show that uniform K-stability is necessary condition for the existence of $f$-extremal metrics on toric manifolds. Furthermore, we show that uniform K-stability is equivalent to properness of relative K-energy.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43536252","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}
Carolyn S. Gordon, Eran Makover, Bjoern Muetzel, David L. Webb
{"title":"Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds","authors":"Carolyn S. Gordon, Eran Makover, Bjoern Muetzel, David L. Webb","doi":"10.2748/tmj/1585101624","DOIUrl":"https://doi.org/10.2748/tmj/1585101624","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"72 1","pages":"127-147"},"PeriodicalIF":0.5,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46253353","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 prove that the higher Nash blowup of a normal toric variety defined over a field of positive characteristic is an isomorphism if and only if it is non-singular. We also extend a result by R. Toh-Yama which shows that higher Nash blowups do not give a one-step resolution of the $A_3$-singularity. These results were previously known only in characteristic zero.
{"title":"Higher Nash blowups of normal toric varieties in prime characteristic","authors":"Daniel Duarte, Luis N'unez-Betancourt","doi":"10.2748/tmj.20200618","DOIUrl":"https://doi.org/10.2748/tmj.20200618","url":null,"abstract":"We prove that the higher Nash blowup of a normal toric variety defined over a field of positive characteristic is an isomorphism if and only if it is non-singular. We also extend a result by R. Toh-Yama which shows that higher Nash blowups do not give a one-step resolution of the $A_3$-singularity. These results were previously known only in characteristic zero.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69154103","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 discuss the Waring rank of binary forms of degree 4 and 5, without multiple factors, and point out unexpected relations to the harmonic cross-ratio, j-invariants and the golden ratio. These computations of ranks for binary forms are used to show that the combinatorics of a line arrangement in the complex projective plane does not determine the Waring rank of the defining equation even in very simple situations.
{"title":"Waring rank of binary forms, harmonic cross-ratio and golden ratio","authors":"A. Dimca, Gabriel Sticlaru","doi":"10.2748/tmj.20210525","DOIUrl":"https://doi.org/10.2748/tmj.20210525","url":null,"abstract":"We discuss the Waring rank of binary forms of degree 4 and 5, without multiple factors, and point out unexpected relations to the harmonic cross-ratio, j-invariants and the golden ratio. These computations of ranks for binary forms are used to show that the combinatorics of a line arrangement in the complex projective plane does not determine the Waring rank of the defining equation even in very simple situations.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46971606","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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