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The Hadwiger Theorem on Convex Functions, I 凸函数的哈德维格定理，I
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-10-16 DOI: 10.1007/s00039-024-00693-8
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
{"title":"The Hadwiger Theorem on Convex Functions, I","authors":"Andrea Colesanti, Monika Ludwig, Fabian Mussnig","doi":"10.1007/s00039-024-00693-8","DOIUrl":"https://doi.org/10.1007/s00039-024-00693-8","url":null,"abstract":"<p>A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on <span>({mathbb{R}}^{n})</span> is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"24 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142439713","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
Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow 凯勒-里奇流膨胀极限的几何正则性
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-10-16 DOI: 10.1007/s00039-024-00694-7
Max Hallgren, Wangjian Jian, Jian Song, Gang Tian
{"title":"Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow","authors":"Max Hallgren, Wangjian Jian, Jian Song, Gang Tian","doi":"10.1007/s00039-024-00694-7","DOIUrl":"https://doi.org/10.1007/s00039-024-00694-7","url":null,"abstract":"<p>We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-<i>W</i><sub>1</sub> distances. In particular, the singular sets of each time slice and its tangent cones are closed and of codimension no less than 4.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"169 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142439806","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
Universality and Sharp Matrix Concentration Inequalities 普遍性与尖锐矩阵集中不等式
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-10-10 DOI: 10.1007/s00039-024-00692-9
Tatiana Brailovskaya, Ramon van Handel
{"title":"Universality and Sharp Matrix Concentration Inequalities","authors":"Tatiana Brailovskaya, Ramon van Handel","doi":"10.1007/s00039-024-00692-9","DOIUrl":"https://doi.org/10.1007/s00039-024-00692-9","url":null,"abstract":"<p>We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields sharp matrix concentration inequalities for general sums of independent random matrices when combined with the Gaussian theory of Bandeira, Boedihardjo, and Van Handel. A key feature of the resulting theory is that it is applicable to a broad class of random matrix models that may have highly nonhomogeneous and dependent entries, which can be far outside the mean-field situation considered in classical random matrix theory. We illustrate the theory in applications to random graphs, matrix concentration inequalities for smallest singular values, sample covariance matrices, strong asymptotic freeness, and phase transitions in spiked models.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"49 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142405019","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
Birkhoff Conjecture for Nearly Centrally Symmetric Domains 近中心对称域的伯克霍夫猜想
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-10-10 DOI: 10.1007/s00039-024-00695-6
V. Kaloshin, C. E. Koudjinan, Ke Zhang
{"title":"Birkhoff Conjecture for Nearly Centrally Symmetric Domains","authors":"V. Kaloshin, C. E. Koudjinan, Ke Zhang","doi":"10.1007/s00039-024-00695-6","DOIUrl":"https://doi.org/10.1007/s00039-024-00695-6","url":null,"abstract":"<p>In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the <i>C</i><sup>0</sup>-integrability condition used in their paper.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"23 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142397722","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
Gromov-Witten Invariants in Complex and Morava-Local K-Theories 复杂和莫拉瓦局域 K 理论中的格罗莫夫-维滕不变式
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-10-07 DOI: 10.1007/s00039-024-00697-4
Mohammed Abouzaid, Mark McLean, Ivan Smith
{"title":"Gromov-Witten Invariants in Complex and Morava-Local K-Theories","authors":"Mohammed Abouzaid, Mark McLean, Ivan Smith","doi":"10.1007/s00039-024-00697-4","DOIUrl":"https://doi.org/10.1007/s00039-024-00697-4","url":null,"abstract":"<p>Given a closed symplectic manifold <i>X</i>, we construct Gromov-Witten-type invariants valued both in (complex) <i>K</i>-theory and in any complex-oriented cohomology theory <span>(mathbb{K})</span> which is <i>K</i><sub><i>p</i></sub>(<i>n</i>)-local for some Morava <i>K</i>-theory <i>K</i><sub><i>p</i></sub>(<i>n</i>). We show that these invariants satisfy a version of the Kontsevich-Manin axioms, extending Givental and Lee’s work for the quantum <i>K</i>-theory of complex projective algebraic varieties. In particular, we prove a Gromov-Witten type splitting axiom, and hence define quantum <i>K</i>-theory and quantum <span>(mathbb{K})</span>-theory as commutative deformations of the corresponding (generalised) cohomology rings of <i>X</i>; the definition of the quantum product involves the formal group of the underlying cohomology theory. The key geometric input of these results is a construction of global Kuranishi charts for moduli spaces of stable maps of arbitrary genus to <i>X</i>. On the algebraic side, in order to establish a common framework covering both ordinary <i>K</i>-theory and <i>K</i><sub><i>p</i></sub>(<i>n</i>)-local theories, we introduce a formalism of ‘counting theories’ for enumerative invariants on a category of global Kuranishi charts.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"205 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142383955","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
Direct Products of Free Groups in Aut(FN) Aut(FN) 中自由基的直积
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-08-05 DOI: 10.1007/s00039-024-00688-5
Martin R. Bridson, Richard D. Wade
{"title":"Direct Products of Free Groups in Aut(FN)","authors":"Martin R. Bridson, Richard D. Wade","doi":"10.1007/s00039-024-00688-5","DOIUrl":"https://doi.org/10.1007/s00039-024-00688-5","url":null,"abstract":"<p>We give a complete description of the embeddings of direct products of nonabelian free groups into Aut(<i>F</i><sub><i>N</i></sub>) and Out(<i>F</i><sub><i>N</i></sub>) when the number of direct factors is maximal. To achieve this, we prove that the image of each such embedding has a canonical fixed point of a particular type in the boundary of Outer space.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"27 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141891851","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
Maximal Multiplicity of Laplacian Eigenvalues in Negatively Curved Surfaces 负弯曲表面中拉普拉奇特征值的最大多重性
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-07-25 DOI: 10.1007/s00039-024-00691-w
Cyril Letrouit, Simon Machado
{"title":"Maximal Multiplicity of Laplacian Eigenvalues in Negatively Curved Surfaces","authors":"Cyril Letrouit, Simon Machado","doi":"10.1007/s00039-024-00691-w","DOIUrl":"https://doi.org/10.1007/s00039-024-00691-w","url":null,"abstract":"<p>In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus <i>g</i>. Our proof relies on a trace argument for the heat kernel, and on the idea of leveraging an <i>r</i>-net in the surface to control this trace. This last idea was introduced in 2021 for similar spectral purposes in the context of graphs of bounded degree. Our method is robust enough to also yield an upper bound on the “approximate multiplicity” of eigenvalues, i.e., the number of eigenvalues in windows of size 1/log<sup><i>β</i></sup>(<i>g</i>), <i>β</i>&gt;0. This work provides new insights on a conjecture by Colin de Verdière and new ways to transfer spectral results from graphs to surfaces.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"57 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141768457","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
Mass Equidistribution for Saito-Kurokawa Lifts 斋藤黑川升降机的质量均衡分布
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-07-23 DOI: 10.1007/s00039-024-00690-x
Jesse Jääsaari, Stephen Lester, Abhishek Saha
{"title":"Mass Equidistribution for Saito-Kurokawa Lifts","authors":"Jesse Jääsaari, Stephen Lester, Abhishek Saha","doi":"10.1007/s00039-024-00690-x","DOIUrl":"https://doi.org/10.1007/s00039-024-00690-x","url":null,"abstract":"<p>Let <i>F</i> be a holomorphic cuspidal Hecke eigenform for <span>(mathrm{Sp}_{4}({mathbb{Z}}))</span> of weight <i>k</i> that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of <i>F</i> equidistributes on the Siegel modular variety as <i>k</i>⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"49 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755300","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
Virtually Free-by-Cyclic Groups 几乎自由的循环群
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-07-22 DOI: 10.1007/s00039-024-00687-6
Dawid Kielak, Marco Linton
{"title":"Virtually Free-by-Cyclic Groups","authors":"Dawid Kielak, Marco Linton","doi":"10.1007/s00039-024-00687-6","DOIUrl":"https://doi.org/10.1007/s00039-024-00687-6","url":null,"abstract":"<p>We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755299","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
Disk-Like Surfaces of Section and Symplectic Capacities 类盘曲面的剖面和交映容积
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-07-16 DOI: 10.1007/s00039-024-00689-4
O. Edtmair
{"title":"Disk-Like Surfaces of Section and Symplectic Capacities","authors":"O. Edtmair","doi":"10.1007/s00039-024-00689-4","DOIUrl":"https://doi.org/10.1007/s00039-024-00689-4","url":null,"abstract":"<p>We prove that the cylindrical capacity of a dynamically convex domain in <span>({mathbb{R}}^{4})</span> agrees with the least symplectic area of a disk-like global surface of section of the Reeb flow on the boundary of the domain. Moreover, we prove the strong Viterbo conjecture for all convex domains in <span>({mathbb{R}}^{4})</span> which are sufficiently <i>C</i><sup>3</sup> close to the round ball. This generalizes a result of Abbondandolo-Bramham-Hryniewicz-Salomão establishing a systolic inequality for such domains.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"59 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141631497","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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