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Conformal Kaehler Submanifolds 共形开普勒子曼形体
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-22 DOI: 10.1007/s00025-024-02203-6
L. J. Alías, S. Chion, M. Dajczer
{"title":"Conformal Kaehler Submanifolds","authors":"L. J. Alías, S. Chion, M. Dajczer","doi":"10.1007/s00025-024-02203-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02203-6","url":null,"abstract":"<p>This paper presents two results in the realm of conformal Kaehler submanifolds. These are conformal immersions of Kaehler manifolds into the standard flat Euclidean space. The proofs are obtained by making a rather strong use of several facts and techniques developed in Chion and Dajczer (Proc Edinb Math Soc 66:810–833, 2023) for the study of isometric immersions of Kaehler manifolds into the standard hyperbolic space.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"56 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153224","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
Some Results of Topological Genericity 拓扑通用性的若干结果
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-22 DOI: 10.1007/s00025-024-02200-9
Christos Pandis
{"title":"Some Results of Topological Genericity","authors":"Christos Pandis","doi":"10.1007/s00025-024-02200-9","DOIUrl":"https://doi.org/10.1007/s00025-024-02200-9","url":null,"abstract":"<p>We prove that a generic function from <span>(bigcap nolimits _{p&lt;1}H^p)</span> has unbounded Taylor coefficients, this applies also to the Taylor coefficients of its derivatives. Results of similar nature are valid when the space <span>(bigcap nolimits _{p&lt;1}H^p)</span> is replaced by <span>(H^p)</span>(<span>(0&lt;p&lt;1)</span>) and by localized versions of such spaces. Moreover, we prove that a generic function from <span>(A(mathbb {D}))</span> has Taylor coefficients outside of <span>(ell ^1)</span>, this applies also to the Taylor coefficients of its derivatives. Lastly, we prove that a generic function from <span>(bigcap nolimits _{p&lt;1}h^p)</span> has a harmonic conjugate that does not belong to any <span>(h^q(q&gt;0))</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"56 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153226","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
Arithmetic Varieties of Numerical Semigroups 数字半群的算术变种
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-22 DOI: 10.1007/s00025-024-02212-5
Manuel B. Branco, Ignacio Ojeda, José Carlos Rosales
{"title":"Arithmetic Varieties of Numerical Semigroups","authors":"Manuel B. Branco, Ignacio Ojeda, José Carlos Rosales","doi":"10.1007/s00025-024-02212-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02212-5","url":null,"abstract":"<p>In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the rooted tree associated with an arithmetic variety. This tree is not locally finite; however, if the Frobenius number is fixed, the tree has finitely many nodes and algorithms can be developed. All algorithms provided in this article include their (non-debugged) implementation in GAP.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"35 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153274","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
Realization of Permutation Modules via Alexandroff Spaces 通过亚历山德罗夫空间实现置换模块
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-22 DOI: 10.1007/s00025-024-02199-z
Cristina Costoya, Rafael Gomes, Antonio Viruel
{"title":"Realization of Permutation Modules via Alexandroff Spaces","authors":"Cristina Costoya, Rafael Gomes, Antonio Viruel","doi":"10.1007/s00025-024-02199-z","DOIUrl":"https://doi.org/10.1007/s00025-024-02199-z","url":null,"abstract":"<p>We raise the question of the realizability of permutation modules in the context of Kahn’s realizability problem for abstract groups and the <i>G</i>-Moore space problem. Specifically, given a finite group <i>G</i>, we consider a collection <span>({M_i}_{i=1}^n)</span> of finitely generated <span>(mathbb {Z}G)</span>-modules that admit a submodule decomposition on which <i>G</i> acts by permuting the summands. Then we prove the existence of connected finite spaces <i>X</i> that realize each <span>(M_i)</span> as its <i>i</i>-th homology, <i>G</i> as its group of self-homotopy equivalences <span>(mathcal {E}(X))</span>, and the action of <i>G</i> on each <span>(M_i)</span> as the action of <span>(mathcal {E}(X))</span> on <span>(H_i(X; mathbb {Z}))</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153223","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
A Diagrammatic Presentation of the Category 3Cob 3Cob 类别图示
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-21 DOI: 10.1007/s00025-024-02201-8
Jovana Nikolić, Zoran Petrić, Mladen Zekić
{"title":"A Diagrammatic Presentation of the Category 3Cob","authors":"Jovana Nikolić, Zoran Petrić, Mladen Zekić","doi":"10.1007/s00025-024-02201-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02201-8","url":null,"abstract":"<p>A category equivalent to the category of 3-dimensional cobordisms is defined in terms of planar diagrams. The operation of composition in this category is completely described via these diagrams.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"222 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153273","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
Harnack Inequality and the Relevant Theorems on Finsler Metric Measure Manifolds 哈纳克不等式和芬斯勒公量测度曼形上的相关定理
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-21 DOI: 10.1007/s00025-024-02196-2
Xinyue Cheng, Yalu Feng
{"title":"Harnack Inequality and the Relevant Theorems on Finsler Metric Measure Manifolds","authors":"Xinyue Cheng, Yalu Feng","doi":"10.1007/s00025-024-02196-2","DOIUrl":"https://doi.org/10.1007/s00025-024-02196-2","url":null,"abstract":"<p>In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler metric measure manifolds with weighted Ricci curvature <span>(textrm{Ric}_{infty })</span> bounded below. Aim on this topic, we first give a volume comparison theorem of Bishop-Gromov type. Then we prove a weighted Poincaré inequality by using Whitney-type coverings technique and give a local uniform Sobolev inequality. Further, we obtain two mean value inequalities for positive subsolutions and supersolutions of a class of parabolic differential equations. From the mean value inequality, we also derive a local gradient estimate for positive solutions to heat equation. Finally, as the application of the mean value inequalities and weighted Poincaré inequality, we get the desired Harnack inequality for positive solutions to heat equation.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"56 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153182","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
Borsik’s Properties of Topological Spaces and Their Applications 博尔西克拓扑空间特性及其应用
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-18 DOI: 10.1007/s00025-024-02194-4
Tomasz Natkaniec
{"title":"Borsik’s Properties of Topological Spaces and Their Applications","authors":"Tomasz Natkaniec","doi":"10.1007/s00025-024-02194-4","DOIUrl":"https://doi.org/10.1007/s00025-024-02194-4","url":null,"abstract":"<p>Let <i>X</i> be an uncountable Polish space. L̆ubica Holá showed recently that there are <span>(2^{mathfrak {c}})</span> quasi-continuous real valued functions defined on the uncountable Polish space <i>X</i> that are not Borel measurable. Inspired by Holá’s result, we are extending it in two directions. First, we prove that if <i>X</i> is an uncountable Polish space and <i>Y</i> is any Hausdorff space with <span>(|Y|ge 2)</span> then the family of all non-Borel measurable quasi-continuous functions has cardinality <span>(ge 2^{{mathfrak {c}}})</span>. Secondly, we show that the family of quasi-continuous non Borel functions from <i>X</i> to <i>Y</i> may contain big algebraic structures.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058995","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
Variations of the Mutual Curvature of Two Orthogonal Non-complementary Distributions 两个正交非互补分布的互曲率变化
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-18 DOI: 10.1007/s00025-024-02185-5
Vladimir Rovenski, Tomasz Zawadzki
{"title":"Variations of the Mutual Curvature of Two Orthogonal Non-complementary Distributions","authors":"Vladimir Rovenski, Tomasz Zawadzki","doi":"10.1007/s00025-024-02185-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02185-5","url":null,"abstract":"<p>On a smooth manifold with distributions <span>(mathcal {D}_1)</span> and <span>(mathcal {D}_2)</span> having trivial intersection, we consider the integral of their mutual curvature, as a functional of Riemannian metrics that make the distributions orthogonal. The mutual curvature is defined as the sum of sectional curvatures of planes spanned by all pairs of vectors from an orthonormal basis, such that one vector of the pair belongs to <span>(mathcal {D}_1)</span> and the second vector belongs to <span>(mathcal {D}_2)</span>. As such, it interpolates between the sectional curvature of a plane field (if both distributions are one-dimensional), and the mixed scalar curvature of a Riemannian almost product structure (if both distributions together span the tangent bundle). We derive Euler–Lagrange equations for the functional, formulated in terms of extrinsic geometry of distributions, i.e., their second fundamental forms and integrability tensors. We give examples of critical metrics for distributions defined on domains of Riemannian submersions, twisted products and <i>f</i>–<i>K</i>-contact manifolds.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141064146","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
Existence Theorems for Parameter Dependent Weakly Continuous Operators with Applications 参数相关弱连续算子的存在定理及其应用
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00025-024-02189-1
Grzegorz Andrzejczak, Marek Galewski, Dumitru Motreanu
{"title":"Existence Theorems for Parameter Dependent Weakly Continuous Operators with Applications","authors":"Grzegorz Andrzejczak, Marek Galewski, Dumitru Motreanu","doi":"10.1007/s00025-024-02189-1","DOIUrl":"https://doi.org/10.1007/s00025-024-02189-1","url":null,"abstract":"<p>The paper presents results on the solvability and parameter dependence for problems driven by weakly continuous potential operators with continuously differentiable and coercive potential. We provide a parametric version on the existence result to nonlinear equations involving coercive and weakly continuous operators. Applications address a variant of elastic beam equation.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"158 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934733","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
Relativity of Reductive Chain Complexes of Non-abelian Simplexes 非阿贝尔简体还原链复合物的相对性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00025-024-02188-2
A. Zuevsky
{"title":"Relativity of Reductive Chain Complexes of Non-abelian Simplexes","authors":"A. Zuevsky","doi":"10.1007/s00025-024-02188-2","DOIUrl":"https://doi.org/10.1007/s00025-024-02188-2","url":null,"abstract":"<p>Chain total double complexes with reductive differentials for non-abelian simplexes with associated spaces are considered. It is conjectured that corresponding relative cohomology is equivalent to the coset space of vanishing functionals over non-vanishing functionals related to differentials of complexes. The conjecture is supported by the theorem for the case of spaces of correlation functions and generalized connections on vertex operator algebra bundles.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"26 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934900","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
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