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Stability of the Faber-Krahn inequality for the short-time Fourier transform 短时傅立叶变换的法布尔-克拉恩不等式的稳定性
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-03-01 DOI: 10.1007/s00222-024-01248-2
Jaime Gómez, André Guerra, João P. G. Ramos, Paolo Tilli
{"title":"Stability of the Faber-Krahn inequality for the short-time Fourier transform","authors":"Jaime Gómez, André Guerra, João P. G. Ramos, Paolo Tilli","doi":"10.1007/s00222-024-01248-2","DOIUrl":"https://doi.org/10.1007/s00222-024-01248-2","url":null,"abstract":"<p>We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit <span>(delta (f;Omega ))</span> which measures by how much the STFT of a function <span>(fin L^{2}(mathbb{R}))</span> fails to be optimally concentrated on an arbitrary set <span>(Omega subset mathbb{R}^{2})</span> of positive, finite measure. We then show that an optimal power of the deficit <span>(delta (f;Omega ))</span> controls both the <span>(L^{2})</span>-distance of <span>(f)</span> to an appropriate class of Gaussians and the distance of <span>(Omega )</span> to a ball, through the Fraenkel asymmetry of <span>(Omega )</span>. Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008704","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
Uniform negative immersions and the coherence of one-relator groups 均匀负沉浸和单链组的一致性
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-29 DOI: 10.1007/s00222-024-01246-4
Larsen Louder, Henry Wilton
{"title":"Uniform negative immersions and the coherence of one-relator groups","authors":"Larsen Louder, Henry Wilton","doi":"10.1007/s00222-024-01246-4","DOIUrl":"https://doi.org/10.1007/s00222-024-01246-4","url":null,"abstract":"<p>Previously, the authors proved that the presentation complex of a one-relator group <span>(G)</span> satisfies a geometric condition called <i>negative immersions</i> if every two-generator, one-relator subgroup of <span>(G)</span> is free. Here, we prove that one-relator groups with negative immersions are coherent, answering a question of Baumslag in this case. Other strong constraints on the finitely generated subgroups also follow such as, for example, the co-Hopf property. The main new theorem strengthens negative immersions to <i>uniform negative immersions</i>, using a rationality theorem proved with linear-programming techniques.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008770","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
The largest prime factor of $n^{2}+1$ and improvements on subexponential $ABC$ $n^{2}+1$ 的最大质因数及对亚指数 $ABC$ 的改进
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-26 DOI: 10.1007/s00222-024-01244-6
Hector Pasten
{"title":"The largest prime factor of $n^{2}+1$ and improvements on subexponential $ABC$","authors":"Hector Pasten","doi":"10.1007/s00222-024-01244-6","DOIUrl":"https://doi.org/10.1007/s00222-024-01244-6","url":null,"abstract":"<p>We combine transcendental methods and the modular approaches to the <span>(ABC)</span> conjecture to show that the largest prime factor of <span>(n^{2}+1)</span> is at least of size <span>((log _{2} n)^{2}/log _{3}n)</span> where <span>(log _{k})</span> is the <span>(k)</span>-th iterate of the logarithm. This gives a substantial improvement on the best available estimates, which are essentially of size <span>(log _{2} n)</span> going back to work of Chowla in 1934. Using the same ideas, we also obtain significant progress on subexpoential bounds for the <span>(ABC)</span> conjecture, which in a case gives the first improvement on a result by Stewart and Yu dating back over two decades. Central to our approach is the connection between Shimura curves and the <span>(ABC)</span> conjecture developed by the author.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969612","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
Virasoro constraints for moduli of sheaves and vertex algebras 剪子和顶点代数模数的维拉索罗约束
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-23 DOI: 10.1007/s00222-024-01245-5
Arkadij Bojko, Woonam Lim, Miguel Moreira
{"title":"Virasoro constraints for moduli of sheaves and vertex algebras","authors":"Arkadij Bojko, Woonam Lim, Miguel Moreira","doi":"10.1007/s00222-024-01245-5","DOIUrl":"https://doi.org/10.1007/s00222-024-01245-5","url":null,"abstract":"<p>In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf theoretic Virasoro constraints in terms of primary states coming from a natural conformal vector in Joyce’s vertex algebra. This shows that Virasoro constraints are preserved under wall-crossing. As an application, we prove the conjectural Virasoro constraints for moduli spaces of torsion-free sheaves on any curve and on surfaces with only <span>((p,p))</span> cohomology classes by reducing the statements to the rank 1 case.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956474","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
A $p$ -adic arithmetic inner product formula p$ 的算术内积公式
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-23 DOI: 10.1007/s00222-024-01243-7
{"title":"A $p$ -adic arithmetic inner product formula","authors":"","doi":"10.1007/s00222-024-01243-7","DOIUrl":"https://doi.org/10.1007/s00222-024-01243-7","url":null,"abstract":"<h3>Abstract</h3> <p>Fix a prime number <span> <span>(p)</span> </span> and let <span> <span>(E/F)</span> </span> be a CM extension of number fields in which <span> <span>(p)</span> </span> splits relatively. Let <span> <span>(pi )</span> </span> be an automorphic representation of a quasi-split unitary group of even rank with respect to <span> <span>(E/F)</span> </span> such that <span> <span>(pi )</span> </span> is ordinary above <span> <span>(p)</span> </span> with respect to the Siegel parabolic subgroup. We construct the cyclotomic <span> <span>(p)</span> </span>-adic <span> <span>(L)</span> </span>-function of <span> <span>(pi )</span> </span>, and a certain generating series of Selmer classes of special cycles on Shimura varieties. We show, under some conditions, that if the vanishing order of the <span> <span>(p)</span> </span>-adic <span> <span>(L)</span> </span>-function is 1, then our generating series is modular and yields explicit nonzero classes (called Selmer theta lifts) in the Selmer group of the Galois representation of <span> <span>(E)</span> </span> associated with <span> <span>(pi )</span> </span>; in particular, the rank of this Selmer group is at least 1. In fact, we prove a precise formula relating the <span> <span>(p)</span> </span>-adic heights of Selmer theta lifts to the derivative of the <span> <span>(p)</span> </span>-adic <span> <span>(L)</span> </span>-function. In parallel to Perrin-Riou’s <span> <span>(p)</span> </span>-adic analogue of the Gross–Zagier formula, our formula is the <span> <span>(p)</span> </span>-adic analogue of the arithmetic inner product formula recently established by Chao Li and the second author.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139951760","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
Existence of harmonic maps and eigenvalue optimization in higher dimensions 高维谐波映射的存在与特征值优化
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-21 DOI: 10.1007/s00222-024-01247-3
Mikhail Karpukhin, Daniel Stern
{"title":"Existence of harmonic maps and eigenvalue optimization in higher dimensions","authors":"Mikhail Karpukhin, Daniel Stern","doi":"10.1007/s00222-024-01247-3","DOIUrl":"https://doi.org/10.1007/s00222-024-01247-3","url":null,"abstract":"<p>We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold <span>((M^{n},g))</span> of dimension <span>(n&gt;2)</span> to any closed, non-aspherical manifold <span>(N)</span> containing no stable minimal two-spheres. In particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special case of the round spheres <span>(N=mathbb{S}^{k})</span>, <span>(kgeqslant 3)</span>, we obtain a distinguished family of nonconstant harmonic maps <span>(Mto mathbb{S}^{k})</span> of index at most <span>(k+1)</span>, with singular set of codimension at least 7 for <span>(k)</span> sufficiently large. Furthermore, if <span>(3leqslant nleqslant 5)</span>, we show that these smooth harmonic maps stabilize as <span>(k)</span> becomes large, and correspond to the solutions of an eigenvalue optimization problem on <span>(M)</span>, generalizing the conformal maximization of the first Laplace eigenvalue on surfaces.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139928480","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
A prismatic approach to crystalline local systems 晶体局部系统的棱柱方法
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-19 DOI: 10.1007/s00222-024-01238-4
Haoyang Guo, Emanuel Reinecke
{"title":"A prismatic approach to crystalline local systems","authors":"Haoyang Guo, Emanuel Reinecke","doi":"10.1007/s00222-024-01238-4","DOIUrl":"https://doi.org/10.1007/s00222-024-01238-4","url":null,"abstract":"<p>Let <span>(X)</span> be a smooth <span>(p)</span>-adic formal scheme. We show that integral crystalline local systems on the generic fiber of <span>(X)</span> are equivalent to prismatic <span>(F)</span>-crystals over the analytic locus of the prismatic site of <span>(X)</span>. As an application, we give a prismatic proof of Fontaine’s <span>(mathrm {C}_{{mathrm {crys}}})</span>-conjecture, for general coefficients, in the relative setting, and allowing ramified base fields. Along the way, we also establish various foundational results for the cohomology of prismatic <span>(F)</span>-crystals, including various comparison theorems, Poincaré duality, and Frobenius isogeny.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139910537","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
Wilson spaces, snaith constructions, and elliptic orientations 威尔逊空间、斯奈斯构造和椭圆定向
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-15 DOI: 10.1007/s00222-024-01239-3
Hood Chatham, Jeremy Hahn, Allen Yuan
{"title":"Wilson spaces, snaith constructions, and elliptic orientations","authors":"Hood Chatham, Jeremy Hahn, Allen Yuan","doi":"10.1007/s00222-024-01239-3","DOIUrl":"https://doi.org/10.1007/s00222-024-01239-3","url":null,"abstract":"<p>We construct a canonical family of even periodic <span>(mathbb{E}_{infty})</span>-ring spectra, with exactly one member of the family for every prime <span>(p)</span> and chromatic height <span>(n)</span>. At height 1 our construction is due to Snaith, who built complex <span>(K)</span>-theory from <span>(mathbb{CP}^{infty})</span>. At height 2 we replace <span>(mathbb{CP}^{infty})</span> with a <span>(p)</span>-local retract of <span>(mathrm{BU} langle 6 rangle )</span>, producing a new theory that orients elliptic, but not generic, height 2 Morava <span>(E)</span>-theories.</p><p>In general our construction exhibits a kind of redshift, whereby <span>(mathrm{BP}langle n-1 rangle )</span> is used to produce a height <span>(n)</span> theory. A familiar sequence of Bocksteins, studied by Tamanoi, Ravenel, Wilson, and Yagita, relates the <span>(K(n))</span>-localization of our height <span>(n)</span> ring to work of Peterson and Westerland building <span>(E_{n}^{hSmathbb{G}^{pm}})</span> from <span>(mathrm{K}(mathbb{Z},n+1))</span>.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139751445","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
Correction to: Linear stability of slowly rotating Kerr black holes 更正：缓慢旋转的克尔黑洞的线性稳定性
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-12 DOI: 10.1007/s00222-024-01240-w
Dietrich Häfner, Peter Hintz, A. Vasy
{"title":"Correction to: Linear stability of slowly rotating Kerr black holes","authors":"Dietrich Häfner, Peter Hintz, A. Vasy","doi":"10.1007/s00222-024-01240-w","DOIUrl":"https://doi.org/10.1007/s00222-024-01240-w","url":null,"abstract":"","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139783773","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
Correction to: Linear stability of slowly rotating Kerr black holes 更正：缓慢旋转的克尔黑洞的线性稳定性
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-12 DOI: 10.1007/s00222-024-01240-w
Dietrich Häfner, Peter Hintz, A. Vasy
{"title":"Correction to: Linear stability of slowly rotating Kerr black holes","authors":"Dietrich Häfner, Peter Hintz, A. Vasy","doi":"10.1007/s00222-024-01240-w","DOIUrl":"https://doi.org/10.1007/s00222-024-01240-w","url":null,"abstract":"","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139843614","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
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