Geometriae Dedicata最新文献

{"title":"New low-genus desingularizations of three Clifford tori and related characterizations.","authors":"Nikolaos Kapouleas, David Wiygul","doi":"10.1007/s10711-026-01100-2","DOIUrl":"https://doi.org/10.1007/s10711-026-01100-2","url":null,"abstract":"<p><p>For each nonnegative integer <i>m</i> we construct in the round three-sphere a closed embedded minimal surface of genus <math><mrow><mn>48</mn> <mi>m</mi> <mo>+</mo> <mn>25</mn></mrow> </math> which can be interpreted as a desingularization of the union of three Clifford tori intersecting pairwise orthogonally, along a total of six great circles. Each such surface is generated, under the action of a group of symmetries, by a disc with hexagonal boundary, all of whose sides are contained in great circles. We prove a uniqueness result for this disc, and, as a corollary, we characterize these surfaces. This characterization implies that similar surfaces we constructed for sufficiently high <i>m</i> by gluing methods, in an earlier article, coincide with the ones here. For low <i>m</i> the surfaces constructed here are new. Similarly, we prove uniqueness of the generating discs for one of two families constructed by Choe and Soret (namely the surfaces they call odd) and show that these surfaces also coincide, when of sufficiently high genus, with surfaces we have constructed by gluing.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"220 5","pages":"59"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13562223/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148957525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A central limit theorem for the winding number of low-lying closed geodesics.","authors":"Elias Dubno","doi":"10.1007/s10711-026-01089-8","DOIUrl":"https://doi.org/10.1007/s10711-026-01089-8","url":null,"abstract":"<p><p>We show that the winding of low-lying closed geodesics on the modular surface has a Gaussian limiting distribution when normalized by any standard notion of length, in contrast to the Cauchy distribution arising when allowing arbitrarily deep excursions into the cusp. In addition, we prove a Berry-Esseen bound and a local limit theorem.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"220 4","pages":"37"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13669119/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149217313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complete characterization of anisotropic geodesics in the Euclidean space.","authors":"Pietro Aldrigo","doi":"10.1007/s10711-026-01111-z","DOIUrl":"https://doi.org/10.1007/s10711-026-01111-z","url":null,"abstract":"<p><p>We provide a characterization of absolutely continuous paths that minimize the anisotropic <i>F</i>-length between two points, where <i>F</i> is a lower semi-continuous, 1-homogeneous positive function defined on <math> <msup><mrow><mi>R</mi></mrow> <mi>n</mi></msup> </math> . The characterization is achieved by establishing a connection between the minimizing paths and the geometry of the anisotropic <i>F</i>-isoperimetric set.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"220 5","pages":"60"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13562349/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148957510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tight contact structures on a family of hyperbolic L-spaces.","authors":"Hyunki Min, Isacco Nonino","doi":"10.1007/s10711-026-01097-8","DOIUrl":"https://doi.org/10.1007/s10711-026-01097-8","url":null,"abstract":"<p><p>We classify tight contact structures on various surgeries on the Whitehead link, which provides the first classification result on an infinite family of hyperbolic L-spaces. We also determine which of the tight contact structures are Stein fillable and which are virtually overtwisted.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"220 4","pages":"45"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13332902/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148392528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Block mapping class groups and their finiteness properties.","authors":"J Aramayona, J Aroca, M Cumplido, R Skipper, X Wu","doi":"10.1007/s10711-025-00985-9","DOIUrl":"https://doi.org/10.1007/s10711-025-00985-9","url":null,"abstract":"<p><p>Given <math><mrow><mi>g</mi> <mo>∈</mo> <mi>N</mi> <mo>∪</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo>}</mo></mrow> </math> , let <math><msub><mi>Σ</mi> <mi>g</mi></msub> </math> denote the closed surface of genus <i>g</i> with a Cantor set removed, if <math><mrow><mi>g</mi> <mo><</mo> <mi>∞</mi></mrow> </math> ; or the blooming Cantor tree, when <math><mrow><mi>g</mi> <mo>=</mo> <mi>∞</mi></mrow> </math> . We construct a family <math><mrow><mi>B</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </math> of subgroups of <math> <mrow><mrow><mspace></mspace> <mtext>Map</mtext> <mspace></mspace></mrow> <mo>(</mo> <msub><mi>Σ</mi> <mi>g</mi></msub> <mo>)</mo></mrow> </math> whose elements preserve a <i>block decomposition</i> of <math><msub><mi>Σ</mi> <mi>g</mi></msub> </math> , and <i>eventually like act</i> like an element of <i>H</i>, where <i>H</i> is a prescribed subgroup of the mapping class group of the block. The group <math><mrow><mi>B</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </math> surjects onto an appropriate symmetric Thompson group of Farley-Hughes; in particular, it answers positively. Our main result asserts that <math><mrow><mi>B</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </math> is of type <math><msub><mi>F</mi> <mi>n</mi></msub> </math> if and only if <i>H</i> is. As a consequence, for every <math><mrow><mi>g</mi> <mo>∈</mo> <mi>N</mi> <mo>∪</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo>}</mo></mrow> </math> and every <math><mrow><mi>n</mi> <mo>≥</mo> <mn>1</mn></mrow> </math> , we construct a subgroup <math><mrow><mi>G</mi> <mo><</mo> <mrow><mspace></mspace> <mtext>Map</mtext> <mspace></mspace></mrow> <mo>(</mo> <msub><mi>Σ</mi> <mi>g</mi></msub> <mo>)</mo></mrow> </math> that is of type <math><msub><mi>F</mi> <mi>n</mi></msub> </math> but not of type <math><msub><mi>F</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>1</mn></mrow> </msub> </math> , and which contains the mapping class group of every compact surface of genus <math><mrow><mo>≤</mo> <mi>g</mi></mrow> </math> and with non-empty boundary.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"219 2","pages":"24"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11836166/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143470021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coarse entropy of metric spaces","authors":"William Geller, Michał Misiurewicz, Damian Sawicki","doi":"10.1007/s10711-024-00925-z","DOIUrl":"https://doi.org/10.1007/s10711-024-00925-z","url":null,"abstract":"<p>Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse entropy and that this value is a coarse invariant. We call this value the coarse entropy of the space and investigate its connections with other properties of the space. We prove that it can only be either zero or infinity, and although for many spaces this dichotomy coincides with the subexponential–exponential growth dichotomy, there is no relation between coarse entropy and volume growth more generally. We completely characterise this dichotomy for spaces with bounded geometry and for quasi-geodesic spaces. As an application, we provide an example where coarse entropy yields an obstruction for a coarse embedding, where such an embedding is not precluded by considerations of volume growth.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255350","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}

{"title":"Geodesic vector fields, induced contact structures and tightness in dimension three","authors":"Tilman Becker","doi":"10.1007/s10711-024-00942-y","DOIUrl":"https://doi.org/10.1007/s10711-024-00942-y","url":null,"abstract":"<p>In this paper, we provide new and simpler proofs of two theorems of Gluck and Harrison on contact structures induced by great circle or line fibrations. Furthermore, we prove that a geodesic vector field whose Jacobi tensor is parallel along flow lines (e.g. if the underlying manifold is locally symmetric) induces a contact structure if the ‘mixed’ sectional curvatures are nonnegative, and if a certain nondegeneracy condition holds. Additionally, we prove that in dimension three, contact structures admitting a Reeb flow which is either periodic, isometric, or free and proper, must be universally tight. In particular, we generalise an earlier result of Geiges and the author, by showing that every contact form on <span>({mathbb {R}}^3)</span> whose Reeb vector field spans a line fibration is necessarily tight. Furthermore, we provide a characterisation of isometric Reeb vector fields. As an application, we recover a result of Kegel and Lange on Seifert fibrations spanned by Reeb vector fields, and we classify closed contact 3-manifolds with isometric Reeb flows (also known as <i>R</i>-contact manifolds) up to diffeomorphism.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"176 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142193929","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}

{"title":"Key varieties for prime $$pmb {mathbb {Q}}$$ -Fano threefolds defined by Freudenthal triple systems","authors":"Hiromichi Takagi","doi":"10.1007/s10711-024-00945-9","DOIUrl":"https://doi.org/10.1007/s10711-024-00945-9","url":null,"abstract":"<p>In this paper, we are concerned with the classification of complex prime <span>(mathbb {Q})</span>-Fano 3-folds of anti-canonical codimension 4 which are produced, as weighted complete intersections of appropriate weighted projectivizations of certain affine varieties related with <span>(mathbb {P}^{1}times mathbb {P}^{1}times mathbb {P}^{1})</span>-fibrations. Such affine varieties or their appropriate weighted projectivizations are called key varieties for prime <span>(mathbb {Q})</span>-Fano 3-folds. We realize that the equations of the key varieties can be described conceptually by Freudenthal triple systems (FTS, for short). The paper consists of two parts. In Part 1, we revisit the general theory of FTS; the main purpose of Part 1 is to derive the conditions of so called strictly regular elements in FTS so as to fit with our description of key varieties. Then, in Part 2, we define several key varieties for prime <span>(mathbb {Q})</span>-Fano 3-folds from the conditions of strictly regular elements in FTS. Among other things obtained in Part 2, we show that there exists a 14-dimensional factorial affine variety <span>(mathfrak {U}_{mathbb {A}}^{14})</span> of codimension 4 in an affine 18-space with only Gorenstein terminal singularities, and we construct examples of prime <span>(mathbb {Q})</span>-Fano 3-folds of No.20544 in as reported by Altınok et al. (The graded ring database, http://www.grdb.co.uk/forms/fano3) as weighted complete intersections of the weighted projectivization of <span>(mathfrak {U}_{mathbb {A}}^{14})</span> in the weighted projective space <span>(mathbb {P}(1^{15},2^{2},3))</span>. We also clarify in Part 2 a relation between <span>(mathfrak {U}_{mathbb {A}}^{14})</span> and the <span>(G_{2}^{(4)})</span>-cluster variety, which is a key variety for prime <span>(mathbb {Q})</span>-Fano 3-folds constructed in Coughlan and Ducat (Compos. Math. 156:1873-1914, 2020).</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"27 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142193947","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}

{"title":"Stable vector bundles on fibered threefolds over a surface","authors":"Tohru Nakashima","doi":"10.1007/s10711-024-00946-8","DOIUrl":"https://doi.org/10.1007/s10711-024-00946-8","url":null,"abstract":"<p>Let <i>X</i> be a smooth projective threefold and let <i>H</i> be an ample line bundle on <i>X</i>. We investigate the existence of vector bundles on <i>X</i> which are <span>(mu )</span>-stable with respect to an ample divisor <span>(H_{epsilon }=H+epsilon D)</span> for sufficiiently small <span>(epsilon &gt;0)</span> where <i>D</i> is a divisor with <span>(Dcdot H^2=0)</span>. In particular, when <i>X</i> is a Fano conic bundle over a rational surface, we show that there exists a family <span>({E_n})</span> of <span>(H_{epsilon })</span>-stable vector bundles with <span>(c_1(E_n)=0)</span> and <span>(c_2(E_n)cdot H)</span> becomes arbitrarily large as <i>n</i> goes to infinity.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"111 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142193952","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}

{"title":"Fundamental regions for non-isometric group actions","authors":"Thomas Leistner, Stuart Teisseire","doi":"10.1007/s10711-024-00944-w","DOIUrl":"https://doi.org/10.1007/s10711-024-00944-w","url":null,"abstract":"<p>We generalise results about isometric group actions on metric spaces and their fundamental regions to the context of merely continuous group actions. In particular, we obtain results that yield the relative compactness of a fundamental region for a cocompact group action. As a consequence, we obtain a criterion for a cocompact cyclic group of semi-Riemannian homotheties to be inessential.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"37 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142193948","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}