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Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when $d = 2,3$ and $u_0$ is radial 当$d = 2,3$和$u_0$为径向时，具有代数非线性的非线性Schrödinger方程的全局适定性和散射
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2019-01-01 DOI: 10.4310/cjm.2019.v7.n3.a2
B. Dodson
{"title":"Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when $d = 2,3$ and $u_0$ is radial","authors":"B. Dodson","doi":"10.4310/cjm.2019.v7.n3.a2","DOIUrl":"https://doi.org/10.4310/cjm.2019.v7.n3.a2","url":null,"abstract":"In this paper we discuss global well-posedness and scattering for some initial value problems that are ˙ H 1 subcritical. We prove global well-posedness and scattering for radial data in H s , s > s c , where the initial value problem is ˙ H s c -critical. We make use of the long time Strichartz estimates of [13] to do this.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 6
Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties 仿射delign - lusztig变体的扭轨积分和不可约分量
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-11-27 DOI: 10.4310/CJM.2020.v8.n1.a3
Rong Zhou, Yihang Zhu
{"title":"Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties","authors":"Rong Zhou, Yihang Zhu","doi":"10.4310/CJM.2020.v8.n1.a3","DOIUrl":"https://doi.org/10.4310/CJM.2020.v8.n1.a3","url":null,"abstract":"We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition functions. As an application we prove a conjecture of Miaofen Chen and Xinwen Zhu, relating the set of irreducible components of an affine Deligne-Lusztig variety modulo the action of the $sigma$-centralizer group to the Mirkovic-Vilonen basis of a certain weight space of a representation of the Langlands dual group.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47424581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 20
Hermitian $K$-theory, Dedekind $zeta$-functions, and quadratic forms over rings of integers in number fields Hermitian$K$理论、Dedekind$zeta$函数和数域中整数环上的二次形式
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-11-09 DOI: 10.4310/cjm.2020.v8.n3.a3
Jonas Irgens Kylling, O. Rondigs, P. Ostvaer
{"title":"Hermitian $K$-theory, Dedekind $zeta$-functions, and quadratic forms over rings of integers in number fields","authors":"Jonas Irgens Kylling, O. Rondigs, P. Ostvaer","doi":"10.4310/cjm.2020.v8.n3.a3","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n3.a3","url":null,"abstract":"We employ the slice spectral sequence, the motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian $K$-groups of rings of integers in number fields. Moreover, we relate the orders of these groups to special values of Dedekind $zeta$-functions for totally real abelian number fields. Our methods apply more readily to the examples of algebraic $K$-theory and higher Witt-theory, and give a complete set of invariants for quadratic forms over rings of integers in number fields.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44044552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Irreducible components of affine Deligne–Lusztig varieties 仿射delign - lusztig品种的不可约成分
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-09-11 DOI: 10.4310/cjm.2022.v10.n2.a2
S. Nie
{"title":"Irreducible components of affine Deligne–Lusztig varieties","authors":"S. Nie","doi":"10.4310/cjm.2022.v10.n2.a2","DOIUrl":"https://doi.org/10.4310/cjm.2022.v10.n2.a2","url":null,"abstract":"By extending the method of semi-modules developed by de Jong,Oort, Viehmann and Hamacher, we introduce a stratification for the affine Deligne-Lusztig variety (in the affine Grassmannian) attached to a basic element. As an application, we verify a conjecture, due to M. Chen and X. Zhu, on the irreducible components of the affine Deligne-Lusztig variety attached to a sum of dominant minuscule coweights.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41659862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 11
Existence of hypersurfaces with prescribed mean curvature I – generic min-max 具有规定平均曲率I的超曲面的存在性-一般最小最大值
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-08-09 DOI: 10.4310/cjm.2020.v8.n2.a2
Xin Zhou, Jonathan J. Zhu
{"title":"Existence of hypersurfaces with prescribed mean curvature I – generic min-max","authors":"Xin Zhou, Jonathan J. Zhu","doi":"10.4310/cjm.2020.v8.n2.a2","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n2.a2","url":null,"abstract":"We prove that, for a generic set of smooth prescription functions $h$ on a closed ambient manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean curvature $h$. The solution is either an embedded minimal hypersurface with integer multiplicity, or a non-minimal almost embedded hypersurface of multiplicity one. \u0000More precisely, we show that our previous min-max theory, developed for constant mean curvature hypersurfaces, can be extended to construct min-max prescribed mean curvature hypersurfaces for certain classes of prescription function, including smooth Morse functions and nonzero analytic functions. In particular we do not need to assume that $h$ has a sign.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44820160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 59
Displacement convexity of Boltzmann’s entropy characterizes the strong energy condition from general relativity 广义相对论强能量条件下Boltzmann熵的位移凸性
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-08-04 DOI: 10.4310/cjm.2020.v8.n3.a4
R. McCann
{"title":"Displacement convexity of Boltzmann’s entropy characterizes the strong energy condition from general relativity","authors":"R. McCann","doi":"10.4310/cjm.2020.v8.n3.a4","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n3.a4","url":null,"abstract":"On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions also make sense in a (nonsmooth) metric measure setting, where they have found powerful applications. This article initiates the development of an analogous theory for lower Ricci curvature bounds in timelike directions on a (globally hyperbolic) Lorentzian manifold. In particular, we lift fractional powers of the Lorentz distance (a.k.a. time separation function) to probability measures on spacetime, and show the strong energy condition of Hawking and Penrose is equivalent to geodesic convexity of the Boltzmann-Shannon entropy there. This represents a significant first step towards a formulation of the strong energy condition and exploration of its consequences in nonsmooth spacetimes, and hints at new connections linking the theory of gravity to the second law of thermodynamics.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47774737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 34
Improved Fourier restriction estimates in higher dimensions 改进的高维傅里叶限制估计
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-07-28 DOI: 10.4310/cjm.2019.v7.n3.a1
J. Hickman, K. Rogers
{"title":"Improved Fourier restriction estimates in higher dimensions","authors":"J. Hickman, K. Rogers","doi":"10.4310/cjm.2019.v7.n3.a1","DOIUrl":"https://doi.org/10.4310/cjm.2019.v7.n3.a1","url":null,"abstract":"We consider Guth's approach to the Fourier restriction problem via polynomial partitioning. By writing out his induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms, we obtain improved bounds for the restriction conjecture, particularly in high dimensions. Consequences for the Kakeya conjecture are also considered.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42819415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 35
On global dynamics of the Maxwell–Klein–Gordon equations 关于Maxwell–Klein–Gordon方程的全局动力学
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-03-30 DOI: 10.4310/cjm.2019.v7.n4.a1
Shiwu Yang, P. Yu
{"title":"On global dynamics of the Maxwell–Klein–Gordon equations","authors":"Shiwu Yang, P. Yu","doi":"10.4310/cjm.2019.v7.n4.a1","DOIUrl":"https://doi.org/10.4310/cjm.2019.v7.n4.a1","url":null,"abstract":"On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing charge and arbitrary large size are unknown. It is conjectured that the solutions disperse as linear waves and enjoy the so-called peeling properties for pointwise estimates. We provide a gauge independent proof of the conjecture.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47167580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 15
Higher $mathcal{L}$-invariants for $mathrm{GL}_3 (mathbb{Q}_p)$ and local-global compatibility $ mathm {GL}_3 (mathbb{Q}_p)$的更高$mathcal{L}$-不变量和局部-全局兼容性
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2018-03-28 DOI: 10.4310/cjm.2020.v8.n4.a2
C. Breuil, Yiwen Ding
{"title":"Higher $mathcal{L}$-invariants for $mathrm{GL}_3 (mathbb{Q}_p)$ and local-global compatibility","authors":"C. Breuil, Yiwen Ding","doi":"10.4310/cjm.2020.v8.n4.a2","DOIUrl":"https://doi.org/10.4310/cjm.2020.v8.n4.a2","url":null,"abstract":"Let $rho_p$ be a $3$-dimensional $p$-adic semi-stable representation of $mathrm{Gal}(overline{mathbb{Q}_p}/mathbb{Q}_p)$ with Hodge-Tate weights $(0,1,2)$ (up to shift) and such that $N^2ne 0$ on $D_{mathrm{st}}(rho_p)$. When $rho_p$ comes from an automorphic representation $pi$ of $G(mathbb{A}_{F^+})$ (for a unitary group $G$ over a totally real field $F^+$ which is compact at infinite places and $mathrm{GL}_3$ at $p$-adic places), we show under mild genericity assumptions that the associated Hecke-isotypic subspaces of the Banach spaces of $p$-adic automorphic forms on $G(mathbb{A}_{F^+}^infty)$ of arbitrary fixed tame level contain (copies of) a unique admissible finite length locally analytic representation of $mathrm{GL}_3(mathbb{Q}_p)$ which only depends on and completely determines $rho_p$.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2018-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90648184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 4
Motivic infinite loop spaces Motivic无限循环空间
IF 1.6 2区 数学
Cambridge Journal of Mathematics Pub Date : 2017-11-14 DOI: 10.4310/cjm.2021.v9.n2.a3
E. Elmanto, Marc Hoyois, Adeel A. Khan, V. Sosnilo, Maria Yakerson
{"title":"Motivic infinite loop spaces","authors":"E. Elmanto, Marc Hoyois, Adeel A. Khan, V. Sosnilo, Maria Yakerson","doi":"10.4310/cjm.2021.v9.n2.a3","DOIUrl":"https://doi.org/10.4310/cjm.2021.v9.n2.a3","url":null,"abstract":"We prove a recognition principle for motivic infinite P1-loop spaces over an infinite perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of E-infinity-spaces. A framed motivic space is a motivic space equipped with transfers along finite syntomic morphisms with trivialized cotangent complex in K-theory. Our main result is that grouplike framed motivic spaces are equivalent to the full subcategory of motivic spectra generated under colimits by suspension spectra. As a consequence, we deduce some representability results for suspension spectra of smooth varieties, and in particular for the motivic sphere spectrum, in terms of Hilbert schemes of points in affine spaces.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2017-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46029627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 43
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