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Geometry of positive scalar curvature on complete manifold 完全流形上正标量曲率的几何
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-01-29 DOI: 10.1515/crelle-2022-0049
Bo Zhu
{"title":"Geometry of positive scalar curvature on complete manifold","authors":"Bo Zhu","doi":"10.1515/crelle-2022-0049","DOIUrl":"https://doi.org/10.1515/crelle-2022-0049","url":null,"abstract":"Abstract In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, we prove a minimal volume growth, an estimate of integral of scalar curvature and width. On higher-dimensional manifold, we obtain a volume growth with a stronger condition.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72575938","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
Scrollar invariants, syzygies and representations of the symmetric group 对称群的滚动不变量、协同和表示
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-01-17 DOI: 10.1515/crelle-2022-0088
W. Castryck, F. Vermeulen, Yongqiang Zhao
{"title":"Scrollar invariants, syzygies and representations of the symmetric group","authors":"W. Castryck, F. Vermeulen, Yongqiang Zhao","doi":"10.1515/crelle-2022-0088","DOIUrl":"https://doi.org/10.1515/crelle-2022-0088","url":null,"abstract":"Abstract We give an explicit minimal graded free resolution, in terms of representations of the symmetric group S d {S_{d}} , of a Galois-theoretic configuration of d points in 𝐏 d - 2 {mathbf{P}^{d-2}} that was studied by Bhargava in the context of ring parametrizations. When applied to the geometric generic fiber of a simply branched degree d cover of 𝐏 1 {mathbf{P}^{1}} by a relatively canonically embedded curve C, our construction gives a new interpretation for the splitting types of the syzygy bundles appearing in its relative minimal resolution. Concretely, our work implies that all these splitting types consist of scrollar invariants of resolvent covers. This vastly generalizes a prior observation due to Casnati, namely that the first syzygy bundle of a degree 4 cover splits according to the scrollar invariants of its cubic resolvent. Our work also shows that the splitting types of the syzygy bundles, together with the multi-set of scrollar invariants, belong to a much larger class of multi-sets of invariants that can be attached to C → 𝐏 1 {Ctomathbf{P}^{1}} : one for each irreducible representation of S d {S_{d}} , i.e., one for each partition of d.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82714407","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
Classifiability of crossed products by nonamenable groups 不可服从群的交叉产物的可分类性
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-01-10 DOI: 10.1515/crelle-2023-0012
Eusebio Gardella, S. Geffen, J. Kranz, P. Naryshkin
{"title":"Classifiability of crossed products by nonamenable groups","authors":"Eusebio Gardella, S. Geffen, J. Kranz, P. Naryshkin","doi":"10.1515/crelle-2023-0012","DOIUrl":"https://doi.org/10.1515/crelle-2023-0012","url":null,"abstract":"Abstract We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable Baumslag–Solitar groups, a large class of amalgamated free products, lattices in many Lie groups, A ~ 2 {widetilde{A}_{2}} -groups, as well as direct products of the above with arbitrary countable groups. As a consequence, crossed products by amenable, minimal and topologically free actions of such groups on compact metric spaces are Kirchberg algebras in the UCT class, and are therefore classified by K-theory.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81600903","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: 9
Local noncollapsing for complex Monge–Ampère equations 复monge - ampantere方程的局部不坍缩
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-01-09 DOI: 10.1515/crelle-2022-0069
B. Guo, Jian Song
{"title":"Local noncollapsing for complex Monge–Ampère equations","authors":"B. Guo, Jian Song","doi":"10.1515/crelle-2022-0069","DOIUrl":"https://doi.org/10.1515/crelle-2022-0069","url":null,"abstract":"Abstract We prove a local volume noncollapsing estimate for Kähler metrics induced from a family of complex Monge–Ampère equations, assuming a local Ricci curvature lower bound. This local volume estimate can be applied to establish various diameter and gradient estimate.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77873705","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: 5
Erratum to Profinite rigidity for twisted Alexander polynomials (J. reine angew. Math. 771 (2021), 171–192) 扭曲亚历山大多项式的极限刚度勘误[j]。数学。771 (2021)，171-192)
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-01-06 DOI: 10.1515/crelle-2021-0079
Jun Ueki
{"title":"Erratum to Profinite rigidity for twisted Alexander polynomials (J. reine angew. Math. 771 (2021), 171–192)","authors":"Jun Ueki","doi":"10.1515/crelle-2021-0079","DOIUrl":"https://doi.org/10.1515/crelle-2021-0079","url":null,"abstract":"Abstract We clarify the definition of the divisorial hull and recollect some basic facts. Then we correct Lemma 4.2 and Theorem 11.2 (1)–(2) in the original article.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72477435","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
Squarefrees are Gaussian in short intervals 在短间隔内，无平方是高斯分布
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-12-22 DOI: 10.1515/crelle-2022-0066
O. Gorodetsky, Alexander P. Mangerel, B. Rodgers
{"title":"Squarefrees are Gaussian in short intervals","authors":"O. Gorodetsky, Alexander P. Mangerel, B. Rodgers","doi":"10.1515/crelle-2022-0066","DOIUrl":"https://doi.org/10.1515/crelle-2022-0066","url":null,"abstract":"Abstract We show that counts of squarefree integers up to X in short intervals of size H tend to a Gaussian distribution as long as H → ∞ {Htoinfty} and H = X o ⁢ ( 1 ) {H=X^{o(1)}} . This answers a question posed by R. R. Hall in 1989. More generally, we prove a variant of Donsker’s theorem, showing that these counts scale to a fractional Brownian motion with Hurst parameter 1 / 4 {1/4} . In fact, we are able to prove these results hold in general for collections of B-free integers as long as the sieving set B satisfies a very mild regularity property, for Hurst parameter varying with the set B.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79750099","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
On quadratically enriched excess and residual intersections 关于二次富集的过剩和剩余交集
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-12-11 DOI: 10.1515/crelle-2023-0041
Tom Bachmann, K. Wickelgren
{"title":"On quadratically enriched excess and residual intersections","authors":"Tom Bachmann, K. Wickelgren","doi":"10.1515/crelle-2023-0041","DOIUrl":"https://doi.org/10.1515/crelle-2023-0041","url":null,"abstract":"Abstract We use recent duality results of Eisenbud and Ulrich to give tools to study quadratically enriched residual intersections when there is no excess bundle. We use this to prove a formula for the Witt-valued Euler number of an almost complete intersection. We give example computations of quadratically enriched excess and residual intersections.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75716100","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: 0
Extended Erratum to A parabolic flow toward solutions of the optimal transportation problem on domains with boundary (J. reine angew. Math. 672 (2012), 127–160) 带边界域上抛物流最优运输问题解的扩展勘误表[j]。数学。672 (2012)，127-160
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-11-24 DOI: 10.1515/crelle-2021-0062
J. Kitagawa
{"title":"Extended Erratum to A parabolic flow toward solutions of the optimal transportation problem on domains with boundary (J. reine angew. Math. 672 (2012), 127–160)","authors":"J. Kitagawa","doi":"10.1515/crelle-2021-0062","DOIUrl":"https://doi.org/10.1515/crelle-2021-0062","url":null,"abstract":"","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77800624","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: 0
On tempered representations 论缓和表征
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-11-23 DOI: 10.1515/crelle-2022-0019
D. Kazhdan, Alexander Yom Din
{"title":"On tempered representations","authors":"D. Kazhdan, Alexander Yom Din","doi":"10.1515/crelle-2022-0019","DOIUrl":"https://doi.org/10.1515/crelle-2022-0019","url":null,"abstract":"Abstract Let G be a unimodular locally compact group. We define a property of irreducible unitary G-representations V which we call c-temperedness, and which for the trivial V boils down to Følner’s condition (equivalent to the trivial V being tempered, i.e. to G being amenable). The property of c-temperedness is a-priori stronger than the property of temperedness. We conjecture that for semisimple groups over local fields temperedness implies c-temperedness. We check the conjecture for a special class of tempered V’s, as well as for all tempered V’s in the cases of G:=SL2⁢(ℝ){G:=mathrm{SL}_{2}({mathbb{R}})} and of G=PGL2⁢(Ω){G=mathrm{PGL}_{2}(Omega)} for a non-Archimedean local field Ω of characteristic 0 and residual characteristic not 2. We also establish a weaker form of the conjecture, involving only K-finite vectors. In the non-Archimedean case, we give a formula expressing the character of a tempered V as an appropriately-weighted conjugation-average of a matrix coefficient of V, generalising a formula of Harish-Chandra from the case when V is square-integrable.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79456972","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: 3
Curvature estimates for 4-dimensional complete gradient expanding Ricci solitons 四维完全梯度展开Ricci孤子的曲率估计
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-11-18 DOI: 10.1515/crelle-2022-0039
H. Cao, Tianbo Liu
{"title":"Curvature estimates for 4-dimensional complete gradient expanding Ricci solitons","authors":"H. Cao, Tianbo Liu","doi":"10.1515/crelle-2022-0039","DOIUrl":"https://doi.org/10.1515/crelle-2022-0039","url":null,"abstract":"Abstract In this paper, we derive curvature estimates for 4-dimensional complete gradient expanding Ricci solitons with nonnegative Ricci curvature (outside a compact set K). More precisely, we prove that the norm of the curvature tensor Rm {mathrm{{Rm}}} and its covariant derivative ∇ ⁡ Rm {nablamathrm{{Rm}}} can be bounded by the scalar curvature R by | Rm | ≤ C a ⁢ R a {|mathrm{{Rm}}|leq C_{a}R^{a}} and | ∇ ⁡ Rm | ≤ C a ⁢ R a {|nablamathrm{{Rm}}|leq C_{a}R^{a}} (on M ∖ K {Msetminus K} ), for any 0 ≤ a < 1 {0leq a<1} and some constant C a > 0 {C_{a}>0} . Moreover, if the scalar curvature has at most polynomial decay at infinity, then | Rm | ≤ C ⁢ R {|mathrm{{Rm}}|leq CR} (on M ∖ K {Msetminus K} ). As an application, it follows that if a 4-dimensional complete gradient expanding Ricci soliton ( M 4 , g , f ) {(M^{4},g,f)} has nonnegative Ricci curvature and finite asymptotic scalar curvature ratio then it has finite asymptotic curvature ratio, hence admits C 1 , α {C^{1,alpha}} asymptotic cones at infinity ( 0 < α < 1 ) {(0<alpha<1)} according to Chen and Deruelle (2015).[21].","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89908050","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: 3
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