Journal of Topology and Analysis最新文献_第5页

Linear isoperimetric inequality for homogeneous Hadamard manifolds 齐次Hadamard流形的线性等周不等式

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2022-03-17 DOI: 10.1142/s1793525323500334

Hjalti Isleifsson

引用次数: 1

Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem 关于偏集的Morse-Bott理论和一个同调Lusternik-Schnirelmann定理

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-12-30 DOI: 10.1142/s1793525321500709

D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera-Lois, J. A. Vilches

引用次数: 0

Macroscopic scalar curvature and codimension 2 width 宏观标量曲率和余维2宽度

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-12-08 DOI: 10.1142/S1793525323500024

H. Alpert, Alexey Balitskiy, L. Guth

引用次数: 1

Fukaya A∞-structures associated to Lefschetz fibrations. V 与Lefschetz纤颤相关的Fukaya A∞结构。V

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-11-29 DOI: 10.1142/s1793525321500588

Paul Seidel

引用次数: 0

Rigidity of mean convex subsets in non-negatively curved RCD spaces and stability of mean curvature bounds 非负弯曲RCD空间中平均凸子集的刚性与平均曲率界的稳定性

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-11-23 DOI: 10.1142/s1793525323500358

C. Ketterer

引用次数: 4

Commutativity of the Haagerup tensor product and base change for operator modules 哈格鲁普张量积的交换性与算子模的基变

IF 0.8 3区数学

Journal of Topology and Analysis Pub Date : 2021-11-15 DOI: 10.1142/s179352532150062x

Tyrone Crisp

引用次数: 0

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":"46 1","pages":""},"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":"58 1","pages":""},"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