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Commentarii Mathematici Helvetici最新文献

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Assouad–Nagata dimension and gap for ordered metric spaces 有序度量空间的Assouad-Nagata维数和间隙
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-09-24 DOI: 10.4171/cmh/549
A. Erschler, I. Mitrofanov
{"title":"Assouad–Nagata dimension and gap for ordered metric spaces","authors":"A. Erschler, I. Mitrofanov","doi":"10.4171/cmh/549","DOIUrl":"https://doi.org/10.4171/cmh/549","url":null,"abstract":"We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true. We formulate a conjectural characterisation of spaces of finite $AN$-dimension, which would yield a gap statement for the efficiency of orders on metric spaces. Under assumption of doubling, we prove a stronger gap phenomenon about all orders on a given metric space.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43013292","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: 4
Numerical characterization of complex torus quotients 复环面商的数值表征
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-09-14 DOI: 10.4171/cmh/543
B. Claudon, Patrick Graf, Henri Guenancia
{"title":"Numerical characterization of complex torus quotients","authors":"B. Claudon, Patrick Graf, Henri Guenancia","doi":"10.4171/cmh/543","DOIUrl":"https://doi.org/10.4171/cmh/543","url":null,"abstract":". This article gives a characterization of quotients of complex tori by finite groups acting freely in codimension two in terms of a numerical vanishing condition on the first and second Chern class. This generalizes results previously obtained by Greb–Kebekus–Peternell in the projective setting, and by Kirschner and the second author in dimension three. As a key ingredient to the proof, we obtain a version of the Bogomolov–Gieseker inequality for stable sheaves on singular spaces, including a discussion of the case of equality.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47778336","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: 5
Fourier non-uniqueness sets from totally real number fields 全实数域的傅立叶非唯一集
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-08-26 DOI: 10.4171/cmh/538
D. Radchenko, Martin Stoller
{"title":"Fourier non-uniqueness sets from totally real number fields","authors":"D. Radchenko, Martin Stoller","doi":"10.4171/cmh/538","DOIUrl":"https://doi.org/10.4171/cmh/538","url":null,"abstract":". Let K be a totally real number field of degree n ≥ 2. The inverse different of K gives rise to a lattice in R n . We prove that the space of Schwartz Fourier eigenfunctions on R n which vanish on the “component-wise square root” of this lattice, is infinite dimensional. The Fourier non-uniqueness set thus obtained is a discrete subset of the union of all spheres √ mS n − 1 for integers m ≥ 0 and, as m → ∞ , there are ∼ c K m n − 1 many points on the m -th sphere for some explicit constant c K , proportional to the square root of the discriminant of K . This contrasts a recent Fourier uniqueness result by Stoller [17, Cor. 1.1]. Using a different construction involving the codifferent of K , we prove an analogue for discrete subsets of ellipsoids. In special cases, these sets also lie on spheres with more densely spaced radii, but with fewer points on each. We also study a related question about existence of Fourier interpolation formulas with nodes “ √ Λ” for general lattices Λ ⊂ R n . Using results about lattices in Lie groups of higher rank we prove that if n ≥ 2 and a certain group Γ Λ ≤ PSL 2 ( R ) n is discrete, then such interpolation formulas cannot exist. Motivated by these more general considerations, we revisit the case of one radial variable and prove, for all n ≥ 5 and all real λ > 2, Fourier interpolation results for sequences of spheres (cid:112) 2 m/λS n − 1 , where m ranges over any fixed cofinite set of non-negative integers. The proof relies on a series of Poincar´e type for Hecke groups of infinite covolume and is similar to the one in [17, § 4].","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":"61 25","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41246446","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: 3
Hamiltonian flows for pseudo-Anosov mapping classes 伪anosov映射类的哈密顿流
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-06-25 DOI: 10.4171/cmh/551
James Farre
{"title":"Hamiltonian flows for pseudo-Anosov mapping classes","authors":"James Farre","doi":"10.4171/cmh/551","DOIUrl":"https://doi.org/10.4171/cmh/551","url":null,"abstract":"For a given pseudo-Anosov homeomorphism $varphi$ of a closed surface $S$, the action of $varphi$ on the Teichm\"uller space $mathcal T(S)$ preserves the Weil-Petersson symplectic form. We give explicit formulae for two invariant functions $mathcal T(S)to mathbb R$ whose symplectic gradients generate autonomous Hamiltonian flows that coincide with the action of $varphi$ at time one. We compute the Poisson bracket between these two functions. This amounts to computing the variation of length of a H\"older cocyle on one lamination along a shear vector field defined by another. For a measurably generic set of laminations, we prove that the variation of length is expressed as the cosine of the angle between the two laminations integrated against the product H\"older distribution, generalizing a result of Kerckhoff. We also obtain rates of convergence for the supports of germs of differentiable paths of measured laminations in the Hausdorff metric on a hyperbolic surface, which may be of independent interest.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47226955","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
Cycle integrals of the $j$-function on Markov geodesics 函数j在马尔可夫测地线上的循环积分
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-06-17 DOI: 10.4171/cmh/535
P. Bengoechea
{"title":"Cycle integrals of the $j$-function on Markov geodesics","authors":"P. Bengoechea","doi":"10.4171/cmh/535","DOIUrl":"https://doi.org/10.4171/cmh/535","url":null,"abstract":"We give asymptotic upper and lower bounds for the real and imaginary parts of cycle integrals of the classical modular j-function along geodesics that correspond to Markov irrationalities.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41499068","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: 1
Boundary singularities in mean curvature flow and total curvature of minimal surface boundaries 平均曲率流中的边界奇异性和最小曲面边界的总曲率
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-06-13 DOI: 10.4171/cmh/542
B. White
{"title":"Boundary singularities in mean curvature flow and total curvature of minimal surface boundaries","authors":"B. White","doi":"10.4171/cmh/542","DOIUrl":"https://doi.org/10.4171/cmh/542","url":null,"abstract":". For hypersurfaces moving by standard mean curvature flow with boundary, we show that if the tangent flow at a boundary singularity is given by a smoothly embedded shrinker, then the shrinker must be non-orientable. We also show that there is an initially smooth surface in R 3 that develops a boundary singularity for which the shrinker is smoothly embedded (and therefore non-orientable). Indeed, we show that there is a nonempty open set of such initial surfaces. Let κ be the largest number with the following property: if M is a minimal surface in R 3 bounded by a smooth simple closed curve of total curvature < κ , then M is a disk. Examples show that κ < 4 π . In this paper, we use mean curvature flow to show that κ > 3 π . We get a slightly larger lower bound for orientable surfaces.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49412718","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
Effective drilling and filling of tame hyperbolic 3-manifolds 有效钻孔和填充驯服双曲3流形
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-04-20 DOI: 10.4171/CMH/536
D. Futer, J. Purcell, S. Schleimer
{"title":"Effective drilling and filling of tame hyperbolic 3-manifolds","authors":"D. Futer, J. Purcell, S. Schleimer","doi":"10.4171/CMH/536","DOIUrl":"https://doi.org/10.4171/CMH/536","url":null,"abstract":"We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In the thin parts of the manifold, we give effective bounds on the change in complex length of a short closed geodesic. These results quantify the filling theorem of Brock and Bromberg, and extend previous results of the authors from finite volume hyperbolic 3-manifolds to any tame hyperbolic 3-manifold. To prove the main results, we assemble tools from Kleinian group theory into a template for transferring theorems about finite-volume manifolds into theorems about infinite-volume manifolds. We also prove and apply an infinite-volume version of the 6-Theorem.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42048255","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: 2
An upper bound on the revised first Betti number and a torus stability result for RCD spaces RCD空间的修正第一Betti数的上界和环面稳定性结果
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-04-13 DOI: 10.4171/CMH/540
Ilaria Mondello, A. Mondino, Raquel Perales
{"title":"An upper bound on the revised first Betti number and a torus stability result for RCD spaces","authors":"Ilaria Mondello, A. Mondino, Raquel Perales","doi":"10.4171/CMH/540","DOIUrl":"https://doi.org/10.4171/CMH/540","url":null,"abstract":"We prove an upper bound on the rank of the abelianised revised fundamental group (called\"revised first Betti number\") of a compact $RCD^{*}(K,N)$ space, in the same spirit of the celebrated Gromov-Gallot upper bound on the first Betti number for a smooth compact Riemannian manifold with Ricci curvature bounded below. When the synthetic lower Ricci bound is close enough to (negative) zero and the aforementioned upper bound on the revised first Betti number is saturated (i.e. equal to the integer part of $N$, denoted by $lfloor N rfloor$), then we establish a torus stability result stating that the space is $lfloor N rfloor$-rectifiable as a metric measure space, and a finite cover must be mGH-close to an $lfloor N rfloor$-dimensional flat torus; moreover, in case $N$ is an integer, we prove that the space itself is bi-H\"older homeomorphic to a flat torus. This second result extends to the class of non-smooth $RCD^{*}(-delta, N)$ spaces a celebrated torus stability theorem by Colding (later refined by Cheeger-Colding).","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47919805","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: 8
Rationality of even-dimensional intersections of two real quadrics 两个实二次曲面偶维交点的合理性
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2021-01-22 DOI: 10.4171/cmh/529
B. Hassett, J. Koll'ar, Y. Tschinkel
{"title":"Rationality of even-dimensional intersections of two real quadrics","authors":"B. Hassett, J. Koll'ar, Y. Tschinkel","doi":"10.4171/cmh/529","DOIUrl":"https://doi.org/10.4171/cmh/529","url":null,"abstract":"We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44611617","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
Skew-amenability of topological groups 拓扑群的偏斜可修性
IF 0.9 3区 数学
Commentarii Mathematici Helvetici Pub Date : 2020-12-17 DOI: 10.4171/CMH/525
K. Juschenko, Friedrich Martin Schneider
{"title":"Skew-amenability of topological groups","authors":"K. Juschenko, Friedrich Martin Schneider","doi":"10.4171/CMH/525","DOIUrl":"https://doi.org/10.4171/CMH/525","url":null,"abstract":"We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in the sense of Bourbaki. We prove characterizations of skew-amenability for topological groups of isometries and automorphisms, clarify the connection with extensive amenability of group actions, establish a Folner-type characterization, and discuss closure properties of the class of skew-amenable topological groups. Moreover, we isolate a dynamical sufficient condition for skew-amenability and provide several concrete variations of this criterion in the context of transformation groups. These results are then used to decide skew-amenability for a number of examples of topological groups built from or related to Thompson's group $F$ and Monod's group of piecewise projective homeomorphisms of the real line.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45447970","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: 6
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