Journal of Topology and Analysis最新文献_第8页

Quantum Speed Limit and Categorical Energy relative to Microlocal Projector 相对于微局部投影仪的量子速度限制和分类能量

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-11-09 DOI: 10.1142/s1793525323500218

Sheng-Fu Chiu

引用次数: 2

K-theory of the maximal and reduced Roe algebras of metric spaces with A-by-CE coarse fibrations 具有A-by-CE粗颤振的度量空间的极大和约化Roe代数的k理论

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-10-29 DOI: 10.1142/s1793525323500073

Liang Guo, Zheng Luo, Qin Wang, Yazhou Zhang

引用次数: 0

The ratio of homology rank to hyperbolic volume 同调阶与双曲体积之比

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-10-28 DOI: 10.1142/s1793525323500176

R. Guzman, P. Shalen

{"title":"The ratio of homology rank to hyperbolic volume","authors":"R. Guzman, P. Shalen","doi":"10.1142/s1793525323500176","DOIUrl":"https://doi.org/10.1142/s1793525323500176","url":null,"abstract":"Under mild topological restrictions, we obtain new linear upper bounds for the dimension of the mod $p$ homology (for any prime $p$) of a finite-volume orientable hyperbolic $3$ manifold $M$ in terms of its volume. A surprising feature of the arguments in the paper is that they require an application of the Four Color Theorem. If $M$ is closed, and either (a) $pi_1(M)$ has no subgroup isomorphic to the fundamental group of a closed, orientable surface of genus $2, 3$ or $4$, or (b) $p = 2$, and $M$ contains no (embedded, two-sided) incompressible surface of genus $2, 3$ or $4$, then $text{dim}, H_1(M;F_p)<157.763 cdot text{vol}(M)$. If $M$ has one or more cusps, we get a very similar bound assuming that $pi_1(M)$ has no subgroup isomorphic to the fundamental group of a closed, orientable surface of genus $g$ for $g = 2, dots,8$. These results should be compared with those of our previous paper $The ratio of homology rank to hyperbolic volume, I$, in which we obtained a bound with a coefficient in the range of $168$ instead of $158$, without a restriction on surface subgroups or incompressible surfaces. In a future paper, using a much more involved argument, we expect to obtain bounds close to those given by the present paper without such a restriction. The arguments also give new linear upper bounds (with constant terms) for the rank of $pi_1(M)$ in terms of $text{vol},M$, assuming that either $pi_1(M)$ is $9$-free, or $M$ is closed and $pi_1(M)$ is $5$-free.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90799648","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

On geodesically reversible Finsler manifolds 关于测地线可逆的Finsler流形

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-10-25 DOI: 10.1142/s1793525321500576

Yong Fang

{"title":"On geodesically reversible Finsler manifolds","authors":"Yong Fang","doi":"10.1142/s1793525321500576","DOIUrl":"https://doi.org/10.1142/s1793525321500576","url":null,"abstract":"A Finsler manifold is said to be geodesically reversible if the reversed curve of any geodesic remains a geometrical geodesic. Well-known examples of geodesically reversible Finsler metrics are Randers metrics with closed [Formula: see text]-forms. Another family of well-known examples are projectively flat Finsler metrics on the [Formula: see text]-sphere that have constant positive curvature. In this paper, we prove some geometrical and dynamical characterizations of geodesically reversible Finsler metrics, and we prove several rigidity results about a family of the so-called Randers-type Finsler metrics. One of our results is as follows: let [Formula: see text] be a Riemannian–Finsler metric on a closed surface [Formula: see text], and [Formula: see text] be a small antisymmetric potential on [Formula: see text] that is a natural generalization of [Formula: see text]-form (see Sec. 1). If the Randers-type Finsler metric [Formula: see text] is geodesically reversible, and the geodesic flow of [Formula: see text] is topologically transitive, then we prove that [Formula: see text] must be a closed [Formula: see text]-form. We also prove that this rigidity result is not true for the family of projectively flat Finsler metrics on the [Formula: see text]-sphere of constant positive curvature.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73529913","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

Periodic solutions of Hilbert’s fourth problem 希尔伯特第四问题的周期解

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-10-22 DOI: 10.1142/s1793525321500552

J. C. Álvarez Paiva, J. Barbosa Gomes

引用次数: 0

Homological Eigenvalues of graph p-Laplacians 图p-拉普拉斯算子的同调特征值

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-10-12 DOI: 10.1142/s1793525323500346

Dong Zhang

{"title":"Homological Eigenvalues of graph p-Laplacians","authors":"Dong Zhang","doi":"10.1142/s1793525323500346","DOIUrl":"https://doi.org/10.1142/s1793525323500346","url":null,"abstract":"Inspired by persistent homology in topological data analysis, we introduce the homological eigenvalues of the graph $p$-Laplacian $Delta_p$, which allows us to analyse and classify non-variational eigenvalues. We show the stability of homological eigenvalues, and we prove that for any homological eigenvalue $lambda(Delta_p)$, the function $pmapsto p(2lambda(Delta_p))^{frac1p}$ is locally increasing, while the function $pmapsto 2^{-p}lambda(Delta_p)$ is locally decreasing. As a special class of homological eigenvalues, the min-max eigenvalues $lambda_1(Delta_p)$, $cdots$, $lambda_k(Delta_p)$, $cdots$, are locally Lipschitz continuous with respect to $pin[1,+infty)$. We also establish the monotonicity of $p(2lambda_k(Delta_p))^{frac1p}$ and $2^{-p}lambda_k(Delta_p)$ with respect to $pin[1,+infty)$. These results systematically establish a refined analysis of $Delta_p$-eigenvalues for varying $p$, which lead to several applications, including: (1) settle an open problem by Amghibech on the monotonicity of some function involving eigenvalues of $p$-Laplacian with respect to $p$; (2) resolve a question asking whether the third eigenvalue of graph $p$-Laplacian is of min-max form; (3) refine the higher order Cheeger inequalities for graph $p$-Laplacians by Tudisco and Hein, and extend the multi-way Cheeger inequality by Lee, Oveis Gharan and Trevisan to the $p$-Laplacian case. Furthermore, for the 1-Laplacian case, we characterize the homological eigenvalues and min-max eigenvalues from the perspective of topological combinatorics, where our idea is similar to the authors' work on discrete Morse theory.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91295862","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

Complete 3-dimensional λ-translators in the Euclidean space ℝ4 完成欧几里得空间中三维λ翻译器

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-10-09 DOI: 10.1142/s1793525321500540

Zhi Li, G. Wei, Gangyi Chen

引用次数: 1

Local Lagrangian Floer Homology of Quasi-Minimally Degenerate Intersections 拟最小简并交点的局部拉格朗日花同调

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-09-08 DOI: 10.1142/s179352532350036x

S. Auyeung

引用次数: 0

On symplectic capacities and their blind spots 论辛能力及其盲点

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-09-04 DOI: 10.1142/s1793525323500127

E. Kerman, Yuanpu Liang

引用次数: 2

An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics 混合锥尖奇异度量空间的l2 - poincar<s:1> - dolbeault引理

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-09-02 DOI: 10.1142/s1793525321500473

Junchao Shentu, Chen Zhao

引用次数: 0