Inventiones mathematicae最新文献

On the existence of minimal expansive solutions to the $N$ -body problem 论N$体问题的最小扩展解的存在性

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-09-12 DOI: 10.1007/s00222-024-01289-7

Davide Polimeni, Susanna Terracini

引用次数: 0

A dichotomy for Hörmander-type oscillatory integral operators 霍曼德型振荡积分算子的二分法

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-09-12 DOI: 10.1007/s00222-024-01288-8

Shaoming Guo, Hong Wang, Ruixiang Zhang

{"title":"A dichotomy for Hörmander-type oscillatory integral operators","authors":"Shaoming Guo, Hong Wang, Ruixiang Zhang","doi":"10.1007/s00222-024-01288-8","DOIUrl":"https://doi.org/10.1007/s00222-024-01288-8","url":null,"abstract":"In this paper, we first generalize the work of Bourgain (Geom. Funct. Anal. 1(4):321–374, 1991) and state a curvature condition for Hörmander-type oscillatory integral operators, which we call Bourgain’s condition. This condition is notably satisfied by the phase functions for the Fourier restriction problem and the Bochner-Riesz problem. We conjecture that for Hörmander-type oscillatory integral operators satisfying Bourgain’s condition, they satisfy the same (L^{p}) bounds as in the Fourier Restriction Conjecture. To support our conjecture, we show that whenever Bourgain’s condition fails, then the (L^{infty } to L^{q}) boundedness always fails for some (q= q(n) > frac{2n}{n-1}), extending Bourgain’s three-dimensional result (Geom. Funct. Anal. 1(4):321–374, 1991). On the other hand, if Bourgain’s condition holds, then we prove (L^{p}) bounds for Hörmander-type oscillatory integral operators for a range of (p) that extends the currently best-known range for the Fourier restriction conjecture in high dimensions, given by Hickman and Zahl (A note on Fourier restriction and nested polynomial wolff axioms, 2020, arXiv:2010.02251). This gives new progress on the Fourier restriction problem, the Bochner-Riesz problem on (mathbb{R}^{n}), the Bochner-Riesz problem on spheres (S^{n}), etc.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223329","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

Trace formulas and inverse spectral theory for generalized indefinite strings 广义不定弦的迹公式和逆谱理论

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-09-05 DOI: 10.1007/s00222-024-01287-9

Jonathan Eckhardt, Aleksey Kostenko

引用次数: 0

The $(2,1)$ -cable of the figure-eight knot is not smoothly slice 八字结的$(2,1)$缆线不是平滑切线

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-09-03 DOI: 10.1007/s00222-024-01286-w

Irving Dai, Sungkyung Kang, Abhishek Mallick, JungHwan Park, Matthew Stoffregen

引用次数: 0

Twisting in Hamiltonian flows and perfect fluids 哈密顿流和完美流体中的扭曲

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-08-28 DOI: 10.1007/s00222-024-01285-x

Theodore D. Drivas, Tarek M. Elgindi, In-Jee Jeong

引用次数: 0

Morse inequalities for ordered eigenvalues of generic self-adjoint families 一般自相关族有序特征值的莫尔斯不等式

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-08-12 DOI: 10.1007/s00222-024-01284-y

Gregory Berkolaiko, Igor Zelenko

{"title":"Morse inequalities for ordered eigenvalues of generic self-adjoint families","authors":"Gregory Berkolaiko, Igor Zelenko","doi":"10.1007/s00222-024-01284-y","DOIUrl":"https://doi.org/10.1007/s00222-024-01284-y","url":null,"abstract":"In many applied problems one seeks to identify and count the critical points of a particular eigenvalue of a smooth parametric family of self-adjoint matrices, with the parameter space often being known and simple, such as a torus. Among particular settings where such a question arises are the Floquet–Bloch decomposition of periodic Schrödinger operators, topology of potential energy surfaces in quantum chemistry, spectral optimization problems such as minimal spectral partitions of manifolds, as well as nodal statistics of graph eigenfunctions. In contrast to the classical Morse theory dealing with smooth functions, the eigenvalues of families of self-adjoint matrices are not smooth at the points corresponding to repeated eigenvalues (called, depending on the application and on the dimension of the parameter space, the diabolical/Dirac/Weyl points or the conical intersections). This work develops a procedure for associating a Morse polynomial to a point of eigenvalue multiplicity; it utilizes the assumptions of smoothness and self-adjointness of the family to provide concrete answers. In particular, we define the notions of non-degenerate topologically critical point and generalized Morse family, establish that generalized Morse families are generic in an appropriate sense, establish a differential first-order conditions for criticality, as well as compute the local contribution of a topologically critical point to the Morse polynomial. Remarkably, the non-smooth contribution to the Morse polynomial turns out to depend only on the size of the eigenvalue multiplicity and the relative position of the eigenvalue of interest and not on the particulars of the operator family; it is expressed in terms of the homologies of Grassmannians.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932689","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 sharp square function estimate for the moment curve in $mathbb{R}^{3}$ $mathbb{R}^{3}$中矩曲线的锐平方函数估计值

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-08-05 DOI: 10.1007/s00222-024-01282-0

Dominique Maldague

引用次数: 0

Long range order for three-dimensional random field Ising model throughout the entire low temperature regime 三维随机场伊辛模型在整个低温体系中的长程有序性

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-07-31 DOI: 10.1007/s00222-024-01283-z

Jian Ding, Yu Liu, Aoteng Xia

引用次数: 0

Purity and 2-Calabi–Yau categories 纯度和 2-Calabi-Yau 类别

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-07-23 DOI: 10.1007/s00222-024-01279-9

Ben Davison

{"title":"Purity and 2-Calabi–Yau categories","authors":"Ben Davison","doi":"10.1007/s00222-024-01279-9","DOIUrl":"https://doi.org/10.1007/s00222-024-01279-9","url":null,"abstract":"For various 2-Calabi–Yau categories (mathscr{C}) for which the classical stack of objects (mathfrak{M}) has a good moduli space (pcolon mathfrak{M}rightarrow mathcal{M}), we establish purity of the mixed Hodge module complex (p_{!}underline{{mathbb{Q}}}_{{mathfrak {M}}}). We do this by using formality in 2CY categories, along with étale neighbourhood theorems for stacks, to prove that the morphism (p) is modelled étale-locally by the semisimplification morphism from the stack of modules of a preprojective algebra. Via the integrality theorem in cohomological Donaldson–Thomas theory we then prove purity of (p_{!}underline{{mathbb{Q}}}_{{mathfrak {M}}}). It follows that the Beilinson–Bernstein–Deligne–Gabber decomposition theorem for the constant sheaf holds for the morphism (p), despite the possibly singular and stacky nature of ({mathfrak {M}}), and the fact that (p) is not proper. We use this to define cuspidal cohomology for ({mathfrak {M}}), which conjecturally provides a complete space of generators for the BPS algebra associated to (mathscr{C}). We prove purity of the Borel–Moore homology of the moduli stack (mathfrak{M}), provided its good moduli space ℳ is projective, or admits a suitable contracting ({mathbb{C}}^{*})-action. In particular, when (mathfrak{M}) is the moduli stack of Gieseker semistable sheaves on a K3 surface, this proves a conjecture of Halpern-Leistner. We use these results to moreover prove purity for several stacks of coherent sheaves that do not admit a good moduli space. Without the usual assumption that (r) and (d) are coprime, we prove that the Borel–Moore homology of the stack of semistable degree (d) rank (r) Higgs sheaves is pure and carries a perverse filtration with respect to the Hitchin base, generalising the usual perverse filtration for the Hitchin system to the case of singular stacks of Higgs sheaves.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776324","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

Asymptotic geometry of lamplighters over one-ended groups 单端群上点灯器的渐近几何

IF 3.1 1区数学

Inventiones mathematicae Pub Date : 2024-07-22 DOI: 10.1007/s00222-024-01278-w

Anthony Genevois, Romain Tessera

{"title":"Asymptotic geometry of lamplighters over one-ended groups","authors":"Anthony Genevois, Romain Tessera","doi":"10.1007/s00222-024-01278-w","DOIUrl":"https://doi.org/10.1007/s00222-024-01278-w","url":null,"abstract":"This article is dedicated to the asymptotic geometry of wreath products (Fwr H := left ( bigoplus _{H} F right ) rtimes H) where (F) is a finite group and (H) is a finitely generated group. Our first main result says that a coarse map from a finitely presented one-ended group to (Fwr H) must land at bounded distance from a left coset of (H). Our second main result, building on the later, is a very restrictive description of quasi-isometries between two lamplighter groups on finitely presented one-ended groups. Third, we obtain a complete classification of these groups up to quasi-isometry. More precisely, given two finite groups (F_{1}), (F_{2}) and two finitely presented one-ended groups (H_{1}), (H_{2}), we show that (F_{1} wr H_{1}) and (F_{2} wr H_{2}) are quasi-isometric if and only if either (i) (H_{1}), (H_{2}) are non-amenable quasi-isometric groups and (|F_{1}|), (|F_{2}|) have the same prime divisors, or (ii) (H_{1}), (H_{2}) are amenable, (|F_{1}|=k^{n_{1}}) and (|F_{2}|=k^{n_{2}}) for some (k,n_{1},n_{2} geq 1), and there exists a quasi-((n_{2}/n_{1}))-to-one quasi-isometry (H_{1} to H_{2}). This can be seen as far reaching extension of a celebrated work of Eskin-Fisher-Whyte who treated the case of (H=mathbb{Z}). Our approach is however fundamentally different, as it crucially exploits the assumption that (H) is one-ended. Our central tool is a new geometric interpretation of lamplighter groups involving natural families of quasi-median spaces.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745937","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