Pub Date : 2023-05-31DOI: 10.1353/ajm.2023.a897493
L. Mari, M. Rigoli, A. G. Setti
abstract:We correct a mistake in our proof of Lemma~2.17. Although we have to strengthen the assumptions therein and, accordingly, in Theorem~2.22, all of the results on the existence and properties of the IMCF are not affected. Minor changes, with no influence elsewhere in the paper, regard Lemma~3.3, Proposition~4.3 and Lemma~5.3.
{"title":"Corrigendum to \"On the 1/H-flow by p-Laplace approximation: new estimates via fake distances under Ricci lower bounds [Amer. J. Math. 144 (2022), no. 3, 779–849]\"","authors":"L. Mari, M. Rigoli, A. G. Setti","doi":"10.1353/ajm.2023.a897493","DOIUrl":"https://doi.org/10.1353/ajm.2023.a897493","url":null,"abstract":"abstract:We correct a mistake in our proof of Lemma~2.17. Although we have to strengthen the assumptions therein and, accordingly, in Theorem~2.22, all of the results on the existence and properties of the IMCF are not affected. Minor changes, with no influence elsewhere in the paper, regard Lemma~3.3, Proposition~4.3 and Lemma~5.3.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46248048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic twists of GL3 × GL2 L-functions","authors":"Yongxiao Lin, P. Michel, W. Sawin","doi":"10.1353/ajm.2023.0015","DOIUrl":"https://doi.org/10.1353/ajm.2023.0015","url":null,"abstract":"","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44706989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract:We classify global solutions of the Monge-Amp`ere equation $det D^2 u=1$ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^{2,alpha}$ estimates for the non-degenerate Monge-Amp`ere equation in convex polygonal domains in $Bbb{R}^2$ provided a globally $C^2$, convex strict subsolution exists.
{"title":"Global C2,α estimates for the Monge-Ampère equation on polygonal domains in the plane","authors":"N. Le, O. Savin","doi":"10.1353/ajm.2023.0004","DOIUrl":"https://doi.org/10.1353/ajm.2023.0004","url":null,"abstract":"Abstract:We classify global solutions of the Monge-Amp`ere equation $det D^2 u=1$ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^{2,alpha}$ estimates for the non-degenerate Monge-Amp`ere equation in convex polygonal domains in $Bbb{R}^2$ provided a globally $C^2$, convex strict subsolution exists.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49381566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract:In this paper, we construct a higher rank Euler system for $Bbb{G}_m$ over a totally real field by using Stickelberger elements. A key ingredient of the construction is to generalize the notion of the characteristic ideal. Under certain technical assumptions, we prove that all higher Fitting ideals of a certain $p$-ramified Iwasawa module are described by analytic invariants canonicallyassociated with Stickelberger elements.
{"title":"A higher rank Euler system for Gm over a totally real field","authors":"Ryotaro Sakamoto","doi":"10.1353/ajm.2023.0001","DOIUrl":"https://doi.org/10.1353/ajm.2023.0001","url":null,"abstract":"Abstract:In this paper, we construct a higher rank Euler system for $Bbb{G}_m$ over a totally real field by using Stickelberger elements. A key ingredient of the construction is to generalize the notion of the characteristic ideal. Under certain technical assumptions, we prove that all higher Fitting ideals of a certain $p$-ramified Iwasawa module are described by analytic invariants canonicallyassociated with Stickelberger elements.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48813961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
abstract:We study the geometry of certain algebraic curves in the moduli space of cubic polynomials, and in the moduli space of quadratic rational maps. Given $kgeq 0$, ($kneq 1$ in the case of quadratic rational maps), we show that the set of conjugacy classes of maps with a prefixed critical point of preperiod $k$, is an algebraic curve that is irreducible (over $Bbb{C}$). We then study a closely related question concerning the irreducibility (over $Bbb{Q}$) of the set of conjugacy classes of unicritical polynomials, of degree $Dgeq 2$, with a preperiodic critical point. Our proofs are purely arithmetic; they rely on a result providing sufficient conditions under which irreducibility over $Bbb{C}$ is equivalent to irreducibility over $Bbb{Q}$, and on a generalized Eisenstein criterion for irreducibility.
{"title":"Prefixed curves in moduli space","authors":"Xavier Buff, A. Epstein, Sarah C. Koch","doi":"10.1353/ajm.2022.0036","DOIUrl":"https://doi.org/10.1353/ajm.2022.0036","url":null,"abstract":"abstract:We study the geometry of certain algebraic curves in the moduli space of cubic polynomials, and in the moduli space of quadratic rational maps. Given $kgeq 0$, ($kneq 1$ in the case of quadratic rational maps), we show that the set of conjugacy classes of maps with a prefixed critical point of preperiod $k$, is an algebraic curve that is irreducible (over $Bbb{C}$). We then study a closely related question concerning the irreducibility (over $Bbb{Q}$) of the set of conjugacy classes of unicritical polynomials, of degree $Dgeq 2$, with a preperiodic critical point. Our proofs are purely arithmetic; they rely on a result providing sufficient conditions under which irreducibility over $Bbb{C}$ is equivalent to irreducibility over $Bbb{Q}$, and on a generalized Eisenstein criterion for irreducibility.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43819349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"American Journal of Mathematics: Founded in 1878 by Johns Hopkins University","authors":"","doi":"10.1353/ajm.2016.0052","DOIUrl":"https://doi.org/10.1353/ajm.2016.0052","url":null,"abstract":"","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2016.0052","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41516769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Singularities of L2-metric in the canonical bundle formula","authors":"S. Takayama","doi":"10.1353/ajm.2022.0042","DOIUrl":"https://doi.org/10.1353/ajm.2022.0042","url":null,"abstract":"abstract:We prove the moduli part in Kawamata's canonical bundle formula admits a natural singular Hermitian metric with vanishing Lelong numbers.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44268862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"In Memoriam: Steve Zelditch 1953–2022","authors":"C. Sogge","doi":"10.1353/ajm.2022.0035","DOIUrl":"https://doi.org/10.1353/ajm.2022.0035","url":null,"abstract":"","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44327016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu Deng, P. Germain, L. Guth, Simon Leo Rydin Myerson
abstract:We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.
{"title":"Strichartz estimates for the Schrödinger equation on non-rectangular two-dimensional tori","authors":"Yu Deng, P. Germain, L. Guth, Simon Leo Rydin Myerson","doi":"10.1353/ajm.2022.0014","DOIUrl":"https://doi.org/10.1353/ajm.2022.0014","url":null,"abstract":"abstract:We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47848660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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