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On global solutions of the obstacle problem 障碍问题的全局解
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-11 DOI: 10.1215/00127094-2022-0078
Simon Eberle, H. Shahgholian, G. Weiss
{"title":"On global solutions of the obstacle problem","authors":"Simon Eberle, H. Shahgholian, G. Weiss","doi":"10.1215/00127094-2022-0078","DOIUrl":"https://doi.org/10.1215/00127094-2022-0078","url":null,"abstract":"Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45303643","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}
引用次数: 7
Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces Kähler流形和极限空间的全纯平分曲率的比较几何
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-06 DOI: 10.1215/00127094-2021-0058
J. Lott
{"title":"Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces","authors":"J. Lott","doi":"10.1215/00127094-2021-0058","DOIUrl":"https://doi.org/10.1215/00127094-2021-0058","url":null,"abstract":"We give an analog of triangle comparison for Kaehler manifolds with a lower bound on the holomorphic bisectional curvature. We show that the condition passes to noncollapsed Gromov-Hausdorff limits. We discuss tangent cones and singular Kaehler spaces.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47820429","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}
引用次数: 4
Winning property of badly approximable points on curves 曲线上严重逼近点的致胜性质
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-05 DOI: 10.1215/00127094-2022-0038
V. Beresnevich, Erez Nesharim, Lei Yang
{"title":"Winning property of badly approximable points on curves","authors":"V. Beresnevich, Erez Nesharim, Lei Yang","doi":"10.1215/00127094-2022-0038","DOIUrl":"https://doi.org/10.1215/00127094-2022-0038","url":null,"abstract":"In this paper we prove that badly approximable points on any analytic non-degenerate curve in $mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching generalisation of Davenport's problem from the 1960s. Amongst various consequences of our main result is a solution to Bugeaud's problem on real numbers badly approximable by algebraic numbers of arbitrary degree.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46161345","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}
引用次数: 6
Log-concavity of matroid h-vectors and mixed Eulerian numbers 矩阵 h 向量和混合欧拉数的对数凹性
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-05 DOI: 10.1215/00127094-2023-0021
A. Berget, Hunter Spink, Dennis Tseng
{"title":"Log-concavity of matroid h-vectors and mixed Eulerian numbers","authors":"A. Berget, Hunter Spink, Dennis Tseng","doi":"10.1215/00127094-2023-0021","DOIUrl":"https://doi.org/10.1215/00127094-2023-0021","url":null,"abstract":"For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain tautological classes in the combinatorial Chow ring $A^bullet(M)$ arising from Grassmannians. Using mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the h-vector of a matroid complex, improving on an old conjecture of Dawson whose proof was announced recently by Ardila, Denham and Huh.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141206465","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}
引用次数: 18
The Noether inequality for algebraic 3 -folds 代数3 -折叠的Noether不等式
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-01 DOI: 10.1215/00127094-2019-0080
J. Chen, Meng Chen, Chen Jiang
{"title":"The Noether inequality for algebraic 3 -folds","authors":"J. Chen, Meng Chen, Chen Jiang","doi":"10.1215/00127094-2019-0080","DOIUrl":"https://doi.org/10.1215/00127094-2019-0080","url":null,"abstract":"We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${rm vol}(X)geq tfrac{4}{3}p_g(X)-{tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)leq 4$ or $p_g(X)geq 21$, where $p_g(X)$ is the geometric genus and ${rm vol}(X)$ is the canonical volume. This inequality is optimal due to known examples found by M. Kobayashi in 1992.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46035330","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}
引用次数: 10
Symmetric Mahler’s conjecture for the volume product in the 3-dimensional case 三维情形下体积积的对称Mahler猜想
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-04-15 DOI: 10.1215/00127094-2019-0072
Hiroshi Iriyeh, Masataka Shibata
{"title":"Symmetric Mahler’s conjecture for the volume product in the 3-dimensional case","authors":"Hiroshi Iriyeh, Masataka Shibata","doi":"10.1215/00127094-2019-0072","DOIUrl":"https://doi.org/10.1215/00127094-2019-0072","url":null,"abstract":"","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48931057","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}
引用次数: 29
Errata for “Mapping class group and a global Torelli theorem for hyperkähler manifolds” by Misha Verbitsky Misha Verbitsky的“映射类群和hyperkähler流形的全局Torelli定理”的更正
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-04-01 DOI: 10.1215/00127094-2020-0016
{"title":"Errata for “Mapping class group and a global Torelli theorem for hyperkähler manifolds” by Misha Verbitsky","authors":"","doi":"10.1215/00127094-2020-0016","DOIUrl":"https://doi.org/10.1215/00127094-2020-0016","url":null,"abstract":"","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47302919","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}
引用次数: 10
On the Beilinson fiber square 在贝林森纤维广场上
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-03-27 DOI: 10.1215/00127094-2022-0037
Benjamin Antieau, A. Mathew, M. Morrow, T. Nikolaus
{"title":"On the Beilinson fiber square","authors":"Benjamin Antieau, A. Mathew, M. Morrow, T. Nikolaus","doi":"10.1215/00127094-2022-0037","DOIUrl":"https://doi.org/10.1215/00127094-2022-0037","url":null,"abstract":"Using topological cyclic homology, we give a refinement of Beilinson's $p$-adic Goodwillie isomorphism between relative continuous $K$-theory and cyclic homology. As a result, we generalize results of Bloch-Esnault-Kerz and Beilinson on the $p$-adic deformations of $K$-theory classes. Furthermore, we prove structural results for the Bhatt-Morrow-Scholze filtration on $TC$ and identify the graded pieces with the syntomic cohomology of Fontaine-Messing.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47405170","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}
引用次数: 21
New incompressible symmetric tensor categories in positive characteristic 新不可压缩对称张量范畴的正特征
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-03-23 DOI: 10.1215/00127094-2022-0030
D. Benson, P. Etingof, V. Ostrik
{"title":"New incompressible symmetric tensor categories in positive characteristic","authors":"D. Benson, P. Etingof, V. Ostrik","doi":"10.1215/00127094-2022-0030","DOIUrl":"https://doi.org/10.1215/00127094-2022-0030","url":null,"abstract":"We propose a method of constructing abelian envelopes of symmetric rigid monoidal Karoubian categories over an algebraically closed field $bf k$. If ${rm char}({bf k})=p>0$, we use this method to construct generalizations ${rm Ver}_{p^n}$, ${rm Ver}_{p^n}^+$ of the incompressible abelian symmetric tensor categories defined in arXiv:1807.05549 for $p=2$ and by Gelfand-Kazhdan and Georgiev-Mathieu for $n=1$. Namely, ${rm Ver}_{p^n}$ is the abelian envelope of the quotient of the category of tilting modules for $SL_2(bf k)$ by the $n$-th Steinberg module, and ${rm Ver}_{p^n}^+$ is its subcategory generated by $PGL_2(bf k)$-modules. We show that ${rm Ver}_{p^n}$ are reductions to characteristic $p$ of Verlinde braided tensor categories in characteristic zero, which explains the notation. We study the structure of these categories in detail, and in particular show that they categorify the real cyclotomic rings $mathbb{Z}[2cos(2pi/p^n)]$, and that ${rm Ver}_{p^n}$ embeds into ${rm Ver}_{p^{n+1}}$. We conjecture that every symmetric tensor category of moderate growth over $bf k$ admits a fiber functor to the union ${rm Ver}_{p^infty}$ of the nested sequence ${rm Ver}_{p}subset {rm Ver}_{p^2}subsetcdots$. This would provide an analog of Deligne's theorem in characteristic zero and a generalization of the result of arXiv:1503.01492, which shows that this conjecture holds for fusion categories, and then moreover the fiber functor lands in ${rm Ver}_p$.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949399","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}
引用次数: 18
Errata to “Discriminants in the Grothendieck ring” “格罗滕迪克环中的判别式”的勘误表
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-03-15 DOI: 10.1215/00127094-2020-0001
R. Vakil, M. Wood
{"title":"Errata to “Discriminants in the Grothendieck ring”","authors":"R. Vakil, M. Wood","doi":"10.1215/00127094-2020-0001","DOIUrl":"https://doi.org/10.1215/00127094-2020-0001","url":null,"abstract":"The definition ofM in Section 1.1 should be the quotient of K0(VarK) by relations of the form [X] − [Y ] whenever X → Y is a radicial surjective morphism of varieties over K, and all further statements in the paper should use this corrected definition. This quotient of the Grothendieck ring is often taken for applications to motivic integration (see [Mus11, Section 7.2] and [CNS18, Section 4.4]). When K has characteristic 0, these additional relations were already trivial in K0(VarK) (e.g. see [Mus11, Prop 7.25]). The motivic measure of point counting over a finite field still factors through this new definition ofM. This correction is necessary so that the proofs in the paper, in particular those of Theorem 1.13 and in Section 5, are correct. The arguments claim equality inM of [X] and [Y ] where we have a morphism X → Y that is bijective on points over any algebraically closed field. Such an argument is valid in the corrected definition ofM above ([Mus11, Remark A.22]), but is not known to be valid in K0(VarK). We thank Margaret Bilu and Sean Howe for pointing out this mistake and the necessary correction. See [BH19] for further discussion of this issue.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49174324","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}
引用次数: 2
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