发布求助
文献互助 智能选刊 最新文献

Geometriae Dedicata最新文献

筛选
英文 中文
The residual set dimension of a generalized apollonian packing 广义阿波罗包装的残集维度
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-03-06 DOI: 10.1007/s10711-024-00899-y
Daniel Lautzenheiser
{"title":"The residual set dimension of a generalized apollonian packing","authors":"Daniel Lautzenheiser","doi":"10.1007/s10711-024-00899-y","DOIUrl":"https://doi.org/10.1007/s10711-024-00899-y","url":null,"abstract":"<p>We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of isometries. This allows for the application of counting methods which admit rigorous upper and lower bounds on the Hausdorff dimension of the residual set of a generalized Apollonian circle packing. This dimension (which also coincides with a critical exponent) is strictly greater than that of the Apollonian packing.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds 平面和双曲 3 维空间上恒定螺距螺旋运动的亚黎曼长度谱
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-26 DOI: 10.1007/s10711-024-00896-1
Marcos Salvai
{"title":"The sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds","authors":"Marcos Salvai","doi":"10.1007/s10711-024-00896-1","DOIUrl":"https://doi.org/10.1007/s10711-024-00896-1","url":null,"abstract":"<p>Let <i>M</i> be an oriented three-dimensional Riemannian manifold of constant sectional curvature <span>(k=0,1,-1)</span> and let <span>(SOleft( Mright) )</span> be its direct orthonormal frame bundle (direct refers to positive orientation), which may be thought of as the set of all positions of a small body in <i>M</i>. Given <span>( lambda in {mathbb {R}})</span>, there is a three-dimensional distribution <span>(mathcal { D}^{lambda })</span> on <span>(SOleft( Mright) )</span> accounting for infinitesimal rototranslations of constant pitch <span>(lambda )</span>. When <span>(lambda ne k^{2})</span>, there is a canonical sub-Riemannian structure on <span>({mathcal {D}}^{lambda })</span>. We present a geometric characterization of its geodesics, using a previous Lie theoretical description. For <span>(k=0,-1)</span>, we compute the sub-Riemannian length spectrum of <span>(left( SOleft( Mright) ,{mathcal {D}} ^{lambda }right) )</span> in terms of the complex length spectrum of <i>M</i> (given by the lengths and the holonomies of the periodic geodesics) when <i>M</i> has positive injectivity radius. In particular, for two complex length isospectral closed hyperbolic 3-manifolds (even if they are not isometric), the associated sub-Riemannian metrics on their direct orthonormal bundles are length isospectral.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Infinitesimal symmetries of bundle gerbes and Courant algebroids 束根和库朗梯形的无限对称性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-26 DOI: 10.1007/s10711-024-00897-0
{"title":"Infinitesimal symmetries of bundle gerbes and Courant algebroids","authors":"","doi":"10.1007/s10711-024-00897-0","DOIUrl":"https://doi.org/10.1007/s10711-024-00897-0","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>M</em> be a smooth manifold and let <span> <span>(chi in Omega ^3(M))</span> </span> be closed differential form with integral periods. We show the Lie 2-algebra <span> <span>(mathbb {L}(C_chi ))</span> </span> of sections of the <span> <span>(chi )</span> </span>-twisted Courant algebroid <span> <span>(C_chi )</span> </span> on <em>M</em> is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an <span> <span>(S^1)</span> </span>-bundle gerbe with connection (over <em>M</em>) whose 3-curvature is <span> <span>(chi )</span> </span>. </p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 family of Andrews–Curtis trivializations via 4-manifold trisections 通过四曲面三等分的安德鲁斯-柯蒂斯三等分家族
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-19 DOI: 10.1007/s10711-024-00891-6
Ethan Romary, Alexander Zupan
{"title":"A family of Andrews–Curtis trivializations via 4-manifold trisections","authors":"Ethan Romary, Alexander Zupan","doi":"10.1007/s10711-024-00891-6","DOIUrl":"https://doi.org/10.1007/s10711-024-00891-6","url":null,"abstract":"<p>An R-link is an <i>n</i>-component link <i>L</i> in <span>(S^3)</span> such that Dehn surgery on <i>L</i> yields <span>(#^n(S^1 times S^2))</span>. Every R-link <i>L</i> gives rise to a geometrically simply-connected homotopy 4-sphere <span>(X_L)</span>, which in turn can be used to produce a balanced presentation of the trivial group. Adapting work of Gompf, Scharlemann, and Thompson, Meier and Zupan produced a family of R-links <i>L</i>(<i>p</i>, <i>q</i>; <i>c</i>/<i>d</i>), where the pairs (<i>p</i>, <i>q</i>) and (<i>c</i>, <i>d</i>) are relatively prime and <i>c</i> is even. Within this family, <span>(L(3,2;2n/(2n+1)))</span> induces the infamous trivial group presentation <span>(langle x,y , | , xyx=yxy, x^{n+1}=y^n rangle )</span>, a popular collection of potential counterexamples to the Andrews–Curtis conjecture for <span>(n ge 3)</span>. In this paper, we use 4-manifold trisections to show that the group presentations corresponding to a different subfamily, <i>L</i>(3, 2; 4/<i>d</i>), are Andrews–Curtis trivial for all <i>d</i>.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139921301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 cyclotomic family of thin hypergeometric monodromy groups in $${text {Sp}}_4({mathbb {R}})$$ $${text {Sp}}_4({mathbb {R}})$$ 中的薄超几何单色群的一个环族
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-19 DOI: 10.1007/s10711-024-00893-4
Simion Filip, Charles Fougeron
{"title":"A cyclotomic family of thin hypergeometric monodromy groups in $${text {Sp}}_4({mathbb {R}})$$","authors":"Simion Filip, Charles Fougeron","doi":"10.1007/s10711-024-00893-4","DOIUrl":"https://doi.org/10.1007/s10711-024-00893-4","url":null,"abstract":"<p>We exhibit an infinite family of discrete subgroups of <span>({{,mathrm{textbf{Sp}},}}_4(mathbb {R}))</span> which have a number of remarkable properties. Our results are established by showing that each group plays ping-pong on an appropriate set of cones. The groups arise as the monodromy of hypergeometric differential equations with parameters <span>(left( tfrac{N-3}{2N},tfrac{N-1}{2N}, tfrac{N+1}{2N}, tfrac{N+3}{2N}right) )</span> at infinity and maximal unipotent monodromy at zero, for any integer <span>(Nge 4)</span>. Additionally, we relate the cones used for ping-pong in <span>(mathbb {R}^4)</span> with crooked surfaces, which we then use to exhibit domains of discontinuity for the monodromy groups in the Lagrangian Grassmannian. These domains of discontinuity lead to uniformizations of variations of Hodge structure with Hodge numbers (1, 1, 1, 1).</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139921249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Complete Calabi–Yau metrics from smoothing Calabi–Yau complete intersections 从平滑 Calabi-Yau 完全交点出发的完全 Calabi-Yau 度量
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-19 DOI: 10.1007/s10711-024-00886-3
Benjy J. Firester
{"title":"Complete Calabi–Yau metrics from smoothing Calabi–Yau complete intersections","authors":"Benjy J. Firester","doi":"10.1007/s10711-024-00886-3","DOIUrl":"https://doi.org/10.1007/s10711-024-00886-3","url":null,"abstract":"<p>We construct complete Calabi–Yau metrics on non-compact manifolds that are smoothings of an initial complete intersection <span>(V_0)</span> that is a Calabi–Yau cone, extending the work of Székelyhidi (Duke Math J 168(14):2651–2700, 2019). The constructed Calabi–Yau manifold has tangent cone at infinity given by <span>({mathbb {C}}times V_0)</span>. This construction produces Calabi–Yau metrics with fibers having varying complex structures and possibly isolated singularities.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139928208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 branched coverings of singular (G, X)-manifolds 论奇异（G，X）-manifolds 的分支覆盖
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-17 DOI: 10.1007/s10711-023-00873-0
Léo Brunswic
{"title":"On branched coverings of singular (G, X)-manifolds","authors":"Léo Brunswic","doi":"10.1007/s10711-023-00873-0","DOIUrl":"https://doi.org/10.1007/s10711-023-00873-0","url":null,"abstract":"<p>Branched coverings boast a rich history, ranging from the ramification of Riemann surfaces to the realization of 3-manifolds as coverings branched over knots and spanning both geometric topology and algebraic geometry. This work delves into branched coverings “à la Fox” of (<i>G</i>, <i>X</i>)-manifolds, encompassing three main avenues: Firstly, we introduce a comprehensive class of singular (<i>G</i>, <i>X</i>)-manifolds, elucidating elementary theory paired with illustrative examples to showcase its efficacy and universality. Secondly, building on Montesinos’ work, we revisit and augment the prevailing knowledge, formulating a Galois theory tailored for such branched coverings. This includes a detailed portrayal of the fiber above branching points. Lastly, we identify local attributes that guarantee the existence of developing maps for singular (<i>G</i>, <i>X</i>)-manifolds within the branched coverings framework. Notably, we pinpoint conditions that ensure the existence of developing maps for these singular manifolds. This research proves especially pertinent for non-metric singular (<i>G</i>, <i>X</i>)-manifolds like those of Lorentzian or projective nature, as discussed by Barbot, Bonsante, Suhyoung Choi, Danciger, Seppi, Schlenker, and the author, among others. While examples are sprinkled throughout, a standout application presented is a uniformization theorem “à la Mess” for singular locally Minkowski manifolds exhibiting BTZ-like singularities.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Unique continuation problem on RCD Spaces. I RCD Spaces 上独特的延续问题。I
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-15 DOI: 10.1007/s10711-024-00890-7
Qin Deng, Xinrui Zhao
{"title":"Unique continuation problem on RCD Spaces. I","authors":"Qin Deng, Xinrui Zhao","doi":"10.1007/s10711-024-00890-7","DOIUrl":"https://doi.org/10.1007/s10711-024-00890-7","url":null,"abstract":"<p>In this note we establish the weak unique continuation theorem for caloric functions on compact <i>RCD</i>(<i>K</i>, 2) spaces and show that there exists an <i>RCD</i>(<i>K</i>, 4) space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point . We also establish frequency estimates for eigenfunctions and caloric functions on the metric horn. In particular, this gives a strong unique continuation type result on the metric horn for harmonic functions with a high rate of decay at the horn tip, where it is known that the standard strong unique continuation property fails.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Borsuk-Ulam Theorem for n-valued maps between surfaces 曲面间 n 值映射的 Borsuk-Ulam 定理
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-14 DOI: 10.1007/s10711-023-00879-8
Vinicius Casteluber Laass, Carolina de Miranda e Pereiro
{"title":"The Borsuk-Ulam Theorem for n-valued maps between surfaces","authors":"Vinicius Casteluber Laass, Carolina de Miranda e Pereiro","doi":"10.1007/s10711-023-00879-8","DOIUrl":"https://doi.org/10.1007/s10711-023-00879-8","url":null,"abstract":"<p>In this work we analysed the validity of a type of Borsuk-Ulam theorem for multimaps between surfaces. We developed an algebraic technique involving braid groups to study this problem for <i>n</i>-valued maps. As a first application we described when the Borsuk-Ulam theorem holds for split and non-split multimaps <span>(phi :X multimap Y)</span> in the following two cases: (<i>i</i>) <i>X</i> is the 2-sphere equipped with the antipodal involution and <i>Y</i> is either a closed surface or the Euclidean plane; (<i>ii</i>) <i>X</i> is a closed surface different from the 2-sphere equipped with a free involution <span>(tau )</span> and <i>Y</i> is the Euclidean plane. The results are exhaustive and in the case (<i>ii</i>) are described in terms of an algebraic condition involving the first integral homology group of the orbit space <span>(X / tau )</span>.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Coregularity of Fano varieties 法诺变种的内核性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2024-02-10 DOI: 10.1007/s10711-023-00882-z
{"title":"Coregularity of Fano varieties","authors":"","doi":"10.1007/s10711-023-00882-z","DOIUrl":"https://doi.org/10.1007/s10711-023-00882-z","url":null,"abstract":"<h3>Abstract</h3> <p>The absolute regularity of a Fano variety, denoted by <span> <span>(hat{textrm{reg}}(X))</span> </span>, is the largest dimension of the dual complex of a log Calabi–Yau structure on <em>X</em>. The absolute coregularity is defined to be <span> <span>$$begin{aligned} hat{textrm{coreg}}(X):= dim X - hat{textrm{reg}}(X)-1. end{aligned}$$</span> </span>The coregularity is the complementary dimension of the regularity. We expect that the coregularity of a Fano variety governs, to a large extent, the geometry of <em>X</em>. In this note, we review the history of Fano varieties, give some examples, survey some theorems, introduce the coregularity, and propose several problems regarding this invariant of Fano varieties.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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