发布求助
文献互助 智能选刊 最新文献

Mathematical Research Letters最新文献

筛选
英文 中文
Planar boundaries and parabolic subgroups 平面边界和抛物线子群
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-04-03 DOI: 10.4310/mrl.2023.v30.n4.a5
G. Christopher Hruska, Genevieve S. Walsh
{"title":"Planar boundaries and parabolic subgroups","authors":"G. Christopher Hruska, Genevieve S. Walsh","doi":"10.4310/mrl.2023.v30.n4.a5","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n4.a5","url":null,"abstract":"We study the Bowditch boundaries of relatively hyperbolic group pairs, focusing on the case where there are no cut points. We show that if $(G, mathcal{P})$ is a rigid relatively hyperbolic group pair whose boundary embeds in $S^2$, then the action on the boundary extends to a convergence group action on $S^2$. More generally, if the boundary is connected and planar with no cut points, we show that every element of $mathcal{P}$ is virtually a surface group. This conclusion is consistent with the conjecture that such a group $G$ is virtually Kleinian. We give numerous examples to show the necessity of our assumptions.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"198 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Cubic graphs induced by bridge trisections 桥式三等分诱导的立方体图形
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-04-03 DOI: 10.4310/mrl.2023.v30.n4.a8
Jeffrey Meier, Abigail Thompson, Alexander Zupan
{"title":"Cubic graphs induced by bridge trisections","authors":"Jeffrey Meier, Abigail Thompson, Alexander Zupan","doi":"10.4310/mrl.2023.v30.n4.a8","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n4.a8","url":null,"abstract":"Every embedded surface $mathcal{K}$ in the $4$-sphere admits a bridge trisection, a decomposition of $(S^4, mathcal{K})$ into three simple pieces. In this case, the surface $mathcal{K}$ is determined by an embedded 1‑complex, called the $1$-<i>skeleton</i> of the bridge trisection. As an abstract graph, the 1‑skeleton is a cubic graph $Gamma$ that inherits a natural Tait coloring, a 3‑coloring of the edge set of $Gamma$ such that each vertex is incident to edges of all three colors. In this paper, we reverse this association: We prove that every Tait-colored cubic graph is isomorphic to the 1‑skeleton of a bridge trisection corresponding to an unknotted surface. When the surface is nonorientable, we show that such an embedding exists for every possible normal Euler number. As a corollary, every tri-plane diagram for a knotted surface can be converted to a tri-plane diagram for an unknotted surface via crossing changes and interior Reidemeister moves. Tools used to prove the main theorem include two new operations on bridge trisections, crosscap summation and tubing, which may be of independent interest.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"74 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Whitney–Graustein homotopy of locally convex curves via a curvature flow 通过曲率流实现局部凸曲线的惠特尼-格劳斯坦同构
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-04-03 DOI: 10.4310/mrl.2023.v30.n4.a3
Laiyuan Gao
{"title":"Whitney–Graustein homotopy of locally convex curves via a curvature flow","authors":"Laiyuan Gao","doi":"10.4310/mrl.2023.v30.n4.a3","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n4.a3","url":null,"abstract":"Let $X_0, tilde{X}$ be two smooth, closed and locally convex curves in the plane with same winding number. A curvature flow with a nonlocal term is constructed to evolve $X_0$ into $tilde{X}$. It is proved that this flow exits globally, preserves both the local convexity and the elastic energy of the evolving curve. If the two curves have same elastic energy then the curvature flow deforms the evolving curve into the target curve $tilde{X}$ as time tends to infinity.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"84 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Computing structure constants for rings of finite rank from minimal free resolutions 从最小自由决议计算有限秩环的结构常数
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2024-04-03 DOI: 10.4310/mrl.2023.v30.n4.a2
Tom Fisher, Lazar Radičević
{"title":"Computing structure constants for rings of finite rank from minimal free resolutions","authors":"Tom Fisher, Lazar Radičević","doi":"10.4310/mrl.2023.v30.n4.a2","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n4.a2","url":null,"abstract":"We show how the minimal free resolution of a set of $n$ points in general position in projective space of dimension $n-2$ explicitly determines structure constants for a ring of rank $n$. This generalises previously known constructions of Levi–Delone–Faddeev and Bhargava in the cases $n = 3, 4, 5$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"52 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 analysis of $1+1$ dimensional quasilinear wave equations 1+1$ 维准线性波方程的几何分析
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a1
Leonardo Enrique Abbrescia, Willie Wai Yeung Wong
{"title":"Geometric analysis of $1+1$ dimensional quasilinear wave equations","authors":"Leonardo Enrique Abbrescia, Willie Wai Yeung Wong","doi":"10.4310/mrl.2023.v30.n3.a1","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a1","url":null,"abstract":"We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not necessarily small. Key to our argument is a form of quasilinear null condition (a “nilpotent structure”) that persists for our class of equations even in the large data setting. This in particular allows us to prove global wellposedness for $C^2$ initial data of moderate decrease, provided the data is sufficiently close to that which generates a simple traveling wave. We take here a geometric approach inspired by works in mathematical relativity and recent works on shock formation for fluid systems. First we recast the equations of motion in terms of a dynamical double-null coordinate system; we show that this formulation semilinearizes our system and decouples the wave variables from the null structure equations. After solving for the wave variables in the double-null coordinate system, we next analyze the null structure equations, using the wave variables as input, to show that the dynamical coordinates are $C^1$ regular and covers the entire spacetime.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Equivariant sheaves on loop spaces 环空间上的等价剪
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a2
Sergey Arkhipov, Sebastian Ørsted
{"title":"Equivariant sheaves on loop spaces","authors":"Sergey Arkhipov, Sebastian Ørsted","doi":"10.4310/mrl.2023.v30.n3.a2","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a2","url":null,"abstract":"Let $X$ be an affine, smooth, and Noetherian scheme over $mathbb{C}$ acted on by an affine algebraic group $G$. Applying the technique developed in $href{https://doi.org/10.48550/arXiv.1807.03266}{[3, }href{ https://doi.org/10.48550/arXiv.1812.03583}{4]}$, we define a dg‑model for the derived category of dg‑modules over the dg‑algebra of differential forms $Omega_X$ on $X$ equivariant with respect to the action of a derived group scheme $(G, Omega_G)$. We compare the obtained dg‑category with the one considered in $href{https://doi.org/10.48550/arXiv.1510.07472}{[2]}$ given by coherent sheaves on the derived Hamiltonian reduction of $T^ast X$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Extendability of automorphisms of K3 surfaces K3 曲面的可扩展性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a9
Yuya Matsumoto
{"title":"Extendability of automorphisms of K3 surfaces","authors":"Yuya Matsumoto","doi":"10.4310/mrl.2023.v30.n3.a9","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a9","url":null,"abstract":"A K3 surface $X$ over a $p$-adic field $K$ is said to have good reduction if it admits a proper smooth model over the ring of integers of $K$. Assuming this, we say that a subgroup $G$ of $operatorname{Aut}(X)$ is extendable if $X$ admits a proper smooth model equipped with $G$-action (compatible with the action on $X$). We show that $G$ is extendable if it is of finite order prime to $p$ and acts symplectically (that is, preserves the global $2$-form on $X$). The proof relies on birational geometry of models of K3 surfaces, and equivariant simultaneous resolutions of certain singularities. We also give some examples of non-extendable actions.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"217 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An example of non-Kähler Calabi–Yau fourfold 非凯勒卡拉比-约四重的一个例子
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a8
Nam-Hoon Lee
{"title":"An example of non-Kähler Calabi–Yau fourfold","authors":"Nam-Hoon Lee","doi":"10.4310/mrl.2023.v30.n3.a8","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a8","url":null,"abstract":"We show that there exists a non-Kähler Calabi–Yau fourfold, constructing an example by smoothing a normal crossing variety.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"34 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties 具有环状连通分量的代数群的全局到局部映射的适当性及其他有限性性质
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a11
Andrei S. Rapinchuk, Igor A. Rapinchuk
{"title":"Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties","authors":"Andrei S. Rapinchuk, Igor A. Rapinchuk","doi":"10.4310/mrl.2023.v30.n3.a11","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a11","url":null,"abstract":"This is a companion paper to $href{ https://doi.org/10.1016/j.jnt.2021.07.001}{[29]}$, where we proved the finiteness of the Tate–Shafarevich group for an arbitrary torus $T$ over a finitely generated field $K$ with respect to any divisorial set $V$ of places of $K$. Here, we extend this result to any $K$-group $D$ whose connected component is a torus (for the same $V$), and as a consequence obtain a finiteness result for the local-to-global conjugacy of maximal tori in reductive groups over finitely generated fields. Moreover, we prove the finiteness of the Tate–Shafarevich group for tori over function fields $K$ of normal varieties defined over base fields of characteristic zero and satisfying Serre’s condition (F), in which case $V$ consists of the discrete valuations associated with the prime divisors on the variety (geometric places). In this situation, we also establish the finiteness of the number of $K$-isomorphism classes of algebraic $K$-tori of a given dimension having good reduction at all $v in V$ , and then discuss ways of extending this result to positive characteristic. Finally, we prove the finiteness of the number of isomorphism classes of forms of an absolutely almost simple group defined over the function field of a complex surface that have good reduction at all geometric places.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"83 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Continuity of the gradient of the fractional maximal operator on $W^{1,1} (mathbb{R}^d)$ 分数最大算子在 $W^{1,1} (mathbb{R}^d)$ 上梯度的连续性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a3
David Beltran, Cristian González-Riquelme, José Madrid, Julian Weigt
{"title":"Continuity of the gradient of the fractional maximal operator on $W^{1,1} (mathbb{R}^d)$","authors":"David Beltran, Cristian González-Riquelme, José Madrid, Julian Weigt","doi":"10.4310/mrl.2023.v30.n3.a3","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a3","url":null,"abstract":"We establish that the map $f mapsto {lvert nabla mathcal{M}_alpha f rvert}$ is continuous from $W^{1,1} (mathbb{R}^d)$ to $L^q (mathbb{R}^d)$, where $alpha in (0, d), q = frac{d}{d-alpha}$ and $M_alpha$ denotes either the centered or non-centered fractional Hardy–Littlewood maximal operator. In particular, we cover the cases $d gt 1$ and $alpha in (0, 1)$ in full generality, for which results were only known for radial functions.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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