发布求助
文献互助 智能选刊 最新文献

Geometric and Functional Analysis最新文献

筛选
英文 中文
Optimal Transport Between Algebraic Hypersurfaces 代数超曲面间的最优传输
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2025-01-22 DOI: 10.1007/s00039-025-00699-w
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
{"title":"Optimal Transport Between Algebraic Hypersurfaces","authors":"Paolo Antonini, Fabio Cavalletti, Antonio Lerario","doi":"10.1007/s00039-025-00699-w","DOIUrl":"https://doi.org/10.1007/s00039-025-00699-w","url":null,"abstract":"<p>What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic projective hypersurfaces.</p><p>First, a natural topological embedding of the space of hypersurfaces of a given degree into the space of measures on the projective space is constructed. Then, the optimal transport problem between hypersurfaces is defined through a constrained dynamical formulation, minimizing the energy of absolutely continuous curves which lie on the image of this embedding. In this way an inner Wasserstein distance on the projective space of homogeneous polynomials is introduced. This distance is finer than the Fubini–Study one.</p><p>The innner Wasserstein distance is complete and geodesic: geodesics corresponds to optimal deformations of one algebraic hypersurface into another one. Outside the discriminant this distance is induced by a smooth Riemannian metric, which is the real part of an explicit Hermitian structure. Moreover, this Hermitian structure is Kähler and the corresponding metric is of Weil–Petersson type.</p><p>To prove these results we develop new techniques, which combine complex and symplectic geometry with optimal transport, and which we expect to be relevant on their own.</p><p>We discuss applications on the regularity of the zeroes of a family of multivariate polynomials and on the condition number of polynomial systems solving.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"27 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142991957","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 the Distance Sets Spanned by Sets of Dimension d/2 in $mathbb{R}^{d}$ $mathbb{R}^{d}$中d/2维集张成的距离集
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2025-01-09 DOI: 10.1007/s00039-024-00696-5
Pablo Shmerkin, Hong Wang
{"title":"On the Distance Sets Spanned by Sets of Dimension d/2 in $mathbb{R}^{d}$","authors":"Pablo Shmerkin, Hong Wang","doi":"10.1007/s00039-024-00696-5","DOIUrl":"https://doi.org/10.1007/s00039-024-00696-5","url":null,"abstract":"<p>We establish the dimension version of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In dimensions <i>d</i>=2 or 3, we obtain the first explicit improvements over the classical 1/2 bound for the dimensions of distance sets of general Borel sets of dimension <i>d</i>/2. For example, we show that the set of distances spanned by a planar Borel set of Hausdorff dimension 1 has Hausdorff dimension at least <span>((sqrt{5}-1)/2approx 0.618)</span>. In higher dimensions we obtain explicit estimates for the lower Minkowski dimension of the distance sets of sets of dimension <i>d</i>/2. These results rely on new estimates for the dimensions of radial projections that may have independent interest.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"8 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142937627","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 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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信